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The methods that we use are estimates on harmonic measure, and the method of layer potentials.\n  The nature of our techniques applied to $D_2$ for $L$ and $R_2$ for $L^t$ leads us to impose a specific size condition on ${\\rm div}b$ in order to obtain solvability."},"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":"1701.08332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-28T23:28:13Z","cross_cats_sorted":[],"title_canon_sha256":"91ac7bd64b47c865ee63989d25f45549483f65ad708527aa017013413cdcdbd2","abstract_canon_sha256":"c704f4928fe2b2f05e6b3d32ec5d0677fae48ae82589822c47f48071b61c65aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:42.134594Z","signature_b64":"KAJmguDyD7WC2c8ekvWC72VN55FavpVvoHm3yOnyWcm1umipDHTIFYpUpoJRUnPYgisgm5bVVOwR8H6PN+tbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6503b4f1e8c013160ab298c8afa3dc900ff0a1e2ea3500612083bbe83d22ea6a","last_reissued_at":"2026-05-18T00:44:42.133943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:42.133943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary value problems in Lipschitz domains for equations with drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Georgios Sakellaris","submitted_at":"2017-01-28T23:28:13Z","abstract_excerpt":"In this work we establish solvability and uniqueness for the $D_2$ Dirichlet problem and the $R_2$ Regularity problem for second order elliptic operators $L=-{\\rm div}(A\\nabla\\cdot)+b\\nabla\\cdot$ in bounded Lipschitz domains, where $b$ is bounded, as well as their adjoint operators $L^t=-{\\rm div}(A^t\\nabla\\cdot)-{\\rm div}(b\\,\\cdot)$. 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