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In our previous paper, we showed the following result: If ${\\mathcal L}_0=\\mbox{div} A^0(x)\\nabla+B^0(x)\\cdot\\nabla$ is a $p$-elliptic operator satisfying certain Carleson condition on $\\nabla A$ and $B$ then the $L^p$ Dirichlet problem for the operator ${\\mathcal L}_0$ is solvable in the upper half-space ${\\mathbb R}^n_+$.\n  In this paper we prove that the $L^p$ solvability is stable under small perturbations of ${\\mathcal L}_0$. That is if ${\\mathcal L}_1$ is anoth"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.08614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-19T16:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"e860a8fbdb4259342b760350d7281b30dd4e18b59657997c1075d84d40a75343","abstract_canon_sha256":"c8aef075e1038406712b3e1eacaa0fc130680ebb3d52bbbcd4a2ba3e4f502c2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:25.746088Z","signature_b64":"pjtUbMS43bWW1cpusqwx5WdjjomWiyL8SDwCSHBCt2o2nNcQ4Qh8zOGbeJL9f/JqFtRIzQS9mV8oyKmBHjElCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"936e33b9cec339fe0ab8741bdb41a5c2079a74acb84ba6266062ddced1e8f404","last_reissued_at":"2026-05-18T00:15:25.745420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:25.745420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbation theory for solutions to second order elliptic operators with complex coefficients and the $L^p$ Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jill Pipher, Martin Dindo\\v{s}","submitted_at":"2018-05-19T16:17:37Z","abstract_excerpt":"We establish a Dahlberg-type perturbation theorem for second order divergence form elliptic operators with complex coefficients. In our previous paper, we showed the following result: If ${\\mathcal L}_0=\\mbox{div} A^0(x)\\nabla+B^0(x)\\cdot\\nabla$ is a $p$-elliptic operator satisfying certain Carleson condition on $\\nabla A$ and $B$ then the $L^p$ Dirichlet problem for the operator ${\\mathcal L}_0$ is solvable in the upper half-space ${\\mathbb R}^n_+$.\n  In this paper we prove that the $L^p$ solvability is stable under small perturbations of ${\\mathcal L}_0$. 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