Paper Citation Record · LEDGER

Boundary estimates and a Wiener criterion for the fractional Laplacian

As of 18 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2107.04364.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2107.04364 v2

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-24T13:43:31.055800Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T19:37:56.102099Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-05T19:37:56.724403Z

Reference resolution

35 of 35 outbound references displayed

verified exact0
verified fuzzy29
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 559eb653-8049-40d1-900a-677ce70a7051 · outbound

This paper cites and G´omez, I., Improvement of Besov regularity for solutions of the fractional Laplacian, Constr.

Boundary estimates and a Wiener criterion for the fractional Laplacian and G´omez, I., Improvement of Besov regularity for solutions of the fractional Laplacian, Constr

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.848877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ed74b896-d376-4221-8e2a-fc546b22c86b · outbound

This paper cites and Ros-Oton, X., Global regularity for the free boundary in the obstacle problem for the fraction Laplacian, Amer.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Ros-Oton, X., Global regularity for the free boundary in the obstacle problem for the fraction Laplacian, Amer

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.844335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e26d1c7f-76e7-4d52-a045-dfa493bab2bc · outbound

This paper cites and Hansen, W., Potential theory.An analytic and probabilistic approach to balayage, Universitext, Springer, Berlin.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Hansen, W., Potential theory.An analytic and probabilistic approach to balayage, Universitext, Springer, Berlin

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.840606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 89245614-988c-4bd5-bc27-2236f0fbabe2 · outbound

This paper cites 123 (1997), 4–80.

Boundary estimates and a Wiener criterion for the fractional Laplacian 123 (1997), 4–80

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.836663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 98f8619b-efb1-4a09-b6fe-d07c9bb68a0f · outbound

This paper cites and Kwa´snicki, M., Estimates and structure of α-harmonic functions, Probab.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Kwa´snicki, M., Estimates and structure of α-harmonic functions, Probab

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.831876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 79640c88-e9db-4b93-b9b2-10e88e0612ba · outbound

This paper cites and Sire, Y., Variational problems with free boundaries for the fractional Laplacian, J.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Sire, Y., Variational problems with free boundaries for the fractional Laplacian, J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.823889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e1aea93d-9c99-4622-af43-1a53fde27013 · outbound

This paper cites and Silvestre, L., Regularity estimates for the solution and the free boundary of the obstacle problem for the fra ctional Lapla- cian, Invent.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Silvestre, L., Regularity estimates for the solution and the free boundary of the obstacle problem for the fra ctional Lapla- cian, Invent

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.820468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 11ad89bd-99f5-434a-8e66-8a52ae8518d4 · outbound

This paper cites and Silvestre, L., An extension problem related to the frac- tional Laplacian, Comm.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Silvestre, L., An extension problem related to the frac- tional Laplacian, Comm

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.812753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 161f12e7-906a-4685-b9b2-f7507d35a1f3 · outbound

This paper cites and Mosco, U., Wiener criteria and energy decay for relaxed Dirichlet problems, Arch.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Mosco, U., Wiener criteria and energy decay for relaxed Dirichlet problems, Arch

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.942349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3ffbdb62-586d-4d65-97fb-7de6b9da70e5 · outbound

This paper cites and Mosco, U., Wiener’s criterion and Γ-convergence, Appl.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Mosco, U., Wiener’s criterion and Γ-convergence, Appl

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.935039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0aa450ff-4892-4775-adc9-4ee2c1f98305 · outbound

This paper cites an unresolved cited work.

Boundary estimates and a Wiener criterion for the fractional Laplacian Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-05-24T13:44:32.930772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f70ade0f-74c3-4c6d-b8c5-05e4f4c1e52f · outbound

This paper cites B., Jerison, D.

Boundary estimates and a Wiener criterion for the fractional Laplacian B., Jerison, D

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.945874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fed12347-5d81-484c-b61a-0aa7ff0aa916 · outbound

This paper cites B., Kenig, C.

Boundary estimates and a Wiener criterion for the fractional Laplacian B., Kenig, C

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.925692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 153a90eb-5e98-466f-80f4-4e5b714ab94d · outbound

This paper cites and Voigt, P., The Dirichlet problem for nonlocal operators, Math.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Voigt, P., The Dirichlet problem for nonlocal operators, Math

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.921666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 05562012-2484-498e-bf89-321cfe0de305 · outbound

This paper cites an unresolved cited work.

Boundary estimates and a Wiener criterion for the fractional Laplacian Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-05-24T13:44:32.915603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9e8dc04b-cf82-4104-a7f8-3fe0caff236b · outbound

This paper cites and Martio, O., Nonlinear Potential Theory of Degenerate Elliptic Equations, 2nd ed., Dover, Mineola, NY.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Martio, O., Nonlinear Potential Theory of Degenerate Elliptic Equations, 2nd ed., Dover, Mineola, NY

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.804956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 77cbd0be-1384-41ef-85b3-fe3da08ed85a · outbound

This paper cites and Jacob, N., On the Dirichlet problem for pseudodiﬀerential op- erators generating Feller semigroups, J.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Jacob, N., On the Dirichlet problem for pseudodiﬀerential op- erators generating Feller semigroups, J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.911987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d053ba1d-79ce-4bac-9daa-9ff85f56a3f4 · outbound

This paper cites and Mal´y, J., The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Mal´y, J., The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.907950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8bf66a42-a1ae-4544-ad4e-cc82552531fb · outbound

This paper cites and Shi, W., Higher regularity for the fractional thin obstacle problem, New York J.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Shi, W., Higher regularity for the fractional thin obstacle problem, New York J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.903380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 03c4f923-0080-4d9d-99ac-0add8b9d46f7 · outbound

This paper cites S., Foundations of modern potential theory, Grundlehren der mathematischen Wissenschaften 180, Springer, New York-Heidelberg.

Boundary estimates and a Wiener criterion for the fractional Laplacian S., Foundations of modern potential theory, Grundlehren der mathematischen Wissenschaften 180, Springer, New York-Heidelberg

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.801517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1947ef65-7f7e-4619-872e-f33a2df8d9ba · outbound

This paper cites and Martio, O., Two theorems of N.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Martio, O., Two theorems of N

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.898493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation feb79fb3-6ef3-41e1-a2d6-7173c6b55b51 · outbound

This paper cites and Weinberger, H.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Weinberger, H

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.894408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 83658db9-3b5a-4698-8fb8-f5f55c9f07cf · outbound

This paper cites G., Regularity at the boundary of solutions of elliptic equations and conformal mapping, Dokl.

Boundary estimates and a Wiener criterion for the fractional Laplacian G., Regularity at the boundary of solutions of elliptic equations and conformal mapping, Dokl

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.887608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation aa34c69e-24d5-4893-bff6-a39eb43d0b4f · outbound

This paper cites G., On the continuity at a boundary point of solutions of quasi- linear elliptic equations, Vestnik Leningrad.

Boundary estimates and a Wiener criterion for the fractional Laplacian G., On the continuity at a boundary point of solutions of quasi- linear elliptic equations, Vestnik Leningrad

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.808932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation eebe3f74-715f-41b4-984c-51e990c45739 · outbound

This paper cites G., Behaviour of solutions to the Dirichlet problem for the bi- harmonic operator at a boundary point, in Equadiﬀ IV (Prague, 1977), pp.

Boundary estimates and a Wiener criterion for the fractional Laplacian G., Behaviour of solutions to the Dirichlet problem for the bi- harmonic operator at a boundary point, in Equadiﬀ IV (Prague, 1977), pp

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.882945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0936f030-0560-492f-a29d-a0ec8927d40c · outbound

This paper cites G., On the Wiener type regularity of a boundary point for the polyharmonic operator, Appl.

Boundary estimates and a Wiener criterion for the fractional Laplacian G., On the Wiener type regularity of a boundary point for the polyharmonic operator, Appl

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.879059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 88e4b2c5-1312-42a8-8cb0-951a869da119 · outbound

This paper cites G., Sobolev Spaces with Applications to Elliptic Partial Diﬀer en- tial Equations, Grundlehren der mathematischen Wissenschaften 342, Springer, Heidelberg.

Boundary estimates and a Wiener criterion for the fractional Laplacian G., Sobolev Spaces with Applications to Elliptic Partial Diﬀer en- tial Equations, Grundlehren der mathematischen Wissenschaften 342, Springer, Heidelberg

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.874693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4b9237cd-56a8-4077-8225-bd4b426b5cf7 · outbound

This paper cites G., Boundary Behavior of Solutions to Elliptic Equations in Gen - eral Domains, EMS Tracts in Mathematics 30, European Math.

Boundary estimates and a Wiener criterion for the fractional Laplacian G., Boundary Behavior of Solutions to Elliptic Equations in Gen - eral Domains, EMS Tracts in Mathematics 30, European Math

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.816779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bfe31b80-a0fb-4fa5-b774-e3e8468c5a7a · outbound

This paper cites an unresolved cited work.

Boundary estimates and a Wiener criterion for the fractional Laplacian Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-05-24T13:44:32.870843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ebccd199-80b6-4025-bfa5-61a00b2ec5de · outbound

This paper cites an unresolved cited work.

Boundary estimates and a Wiener criterion for the fractional Laplacian Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-05-24T13:44:32.867240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 868e9bbb-6355-43d5-a0ec-923879cc87bc · outbound

This paper cites an unresolved cited work.

Boundary estimates and a Wiener criterion for the fractional Laplacian Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-05-24T13:44:32.863701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 069e9c0f-d7ca-4c96-9bdc-8026c5d6fd88 · outbound

This paper cites and Serra, J., The Dirichlet problem for the fractional Lapla- cian: regularity up to the boundary, J.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Serra, J., The Dirichlet problem for the fractional Lapla- cian: regularity up to the boundary, J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.826973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1601d3fd-f29f-4682-be20-c71cfd32e047 · outbound

This paper cites and Serra, J., The Pohozaev identity for the fractional Lapla- cian, Arch.

Boundary estimates and a Wiener criterion for the fractional Laplacian and Serra, J., The Pohozaev identity for the fractional Lapla- cian, Arch

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.860135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 921c878e-3aa2-47cb-b259-82e67dd2360c · outbound

This paper cites Pure Appl.

Boundary estimates and a Wiener criterion for the fractional Laplacian Pure Appl

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T13:44:32.856366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0e65c0c1-d01b-4e42-9caf-99897c0f79cb · outbound

This paper cites an unresolved cited work.

Boundary estimates and a Wiener criterion for the fractional Laplacian Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-05-24T13:44:32.852495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

Observation 0b19c761-dc90-4c6e-813f-1599fa228f5d · inbound

Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation cites this paper.

Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation Boundary estimates and a Wiener criterion for the fractional Laplacian

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-05T19:37:56.738305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.