Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase

Xingchen Zhou

Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2311.13867 v1 pith:ISP5FALR submitted 2023-11-23 math.AP

Xingchen Zhou This is my paper · ORCID

classification math.AP

keywords phaselipschitzsolutionscurvatureequationestimatesfracinterior

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

We establish a prior interior $C^{1,1}$ estimates for convex solutions and supercritical phase solutions to the Lagrangian mean curvature equation with sharp Lipschitz phase. Counter-examples exist when the phase is H\"{o}lder continuous but not Lipschitz. As an application we obtain interior $C^{2,\alpha}$ regularity for $C^0$ viscosity solutions on the first phase interval $((n-2)\frac\pi2,n\frac\pi2)$.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Removing singularities for fully nonlinear PDEs
math.AP 2024-11 conditional novelty 6.0 of 10

Half-line singularities of viscosity solutions are removable for fully nonlinear elliptic PDEs with a Jacobi inequality, proven by a doubling argument; the single-side version is new.

Pith tools