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Arendt","submitted_at":"2018-03-20T10:44:53Z","abstract_excerpt":"Consider the Dirichlet problem with respect to an elliptic operator \\[ A = - \\sum_{k,l=1}^d \\partial_k \\, a_{kl} \\, \\partial_l\n  - \\sum_{k=1}^d \\partial_k \\, b_k\n  + \\sum_{k=1}^d c_k \\, \\partial_k\n  + c_0 \\] on a bounded Wiener regular open set $\\Omega \\subset R^d$, where $a_{kl}, c_k \\in L_\\infty(\\Omega,R)$ and $b_k,c_0 \\in L_\\infty(\\Omega,C)$. Suppose that the associated operator on $L_2(\\Omega)$ with Dirichlet boundary conditions is invertible. Then we show that for all $\\varphi \\in C(\\partial \\Omega)$ there exists a unique $u \\in C(\\overline \\Omega) \\cap H^1_{\\rm loc}(\\Omega)$ such that $u"},"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":"1803.07357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-20T10:44:53Z","cross_cats_sorted":[],"title_canon_sha256":"816c37977cf1d87538c91bb0f82e8401f73ca63ebbcca12f9467c3e4b5e00337","abstract_canon_sha256":"db3f5a1e1ececb1c9834afbb3b20b99730b62b1e47483bff51b2461fb8b3c94c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:33.555933Z","signature_b64":"03JbWk09IOnLfRPcLANe0Sh8T0WpYlecRMJoD4Y4o+ov5VHMuwM36WBnVApqlDT+VL2gsd+HlBOACI/gevjWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b09e652eab65018b2009d8dbec443331e7fdd7dc3d2acc6d92893ccba67acdc5","last_reissued_at":"2026-05-18T00:20:33.555229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:33.555229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Dirichlet problem without the maximum principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.F.M. ter Elst, W. Arendt","submitted_at":"2018-03-20T10:44:53Z","abstract_excerpt":"Consider the Dirichlet problem with respect to an elliptic operator \\[ A = - \\sum_{k,l=1}^d \\partial_k \\, a_{kl} \\, \\partial_l\n  - \\sum_{k=1}^d \\partial_k \\, b_k\n  + \\sum_{k=1}^d c_k \\, \\partial_k\n  + c_0 \\] on a bounded Wiener regular open set $\\Omega \\subset R^d$, where $a_{kl}, c_k \\in L_\\infty(\\Omega,R)$ and $b_k,c_0 \\in L_\\infty(\\Omega,C)$. Suppose that the associated operator on $L_2(\\Omega)$ with Dirichlet boundary conditions is invertible. 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