{"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 ${\\mathcal L}_0$. That is if ${\\mathcal L}_1$ is anoth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08614","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}