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The class of nonlocal operators considered here are defined, via Dirichlet forms, by kernels $K(x,y)$ bounded from above and below by $|x-y|^{N+2s}$, with $s\\in (0,1)$. The entries in the equations are in some Morrey spaces and the underline domain $\\Omega$ satisfies some mild regularity assumptions. In the particular case of the fractional Laplacian, our results are new. When $K$ defines a non"},"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":"1711.02206","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-06T22:48:28Z","cross_cats_sorted":[],"title_canon_sha256":"a84b53aa50321ae05d9ee24e44ed231b579132dfde7dd84777bb44e8c6019c65","abstract_canon_sha256":"ab997039a5b9cb1dcd096fd64aab1bf2a5a50ca5fe99882332ea9b1eb2b9071f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:08.404418Z","signature_b64":"Npi0+dkX+hzfGQtonkuKXbgOeet0embsaz74HL0w36RS4TkAVahihPxgAT5f1CcPBzfMXo5fhH3M0cB5PAkcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d8e38525ddf418980eaf29e9f9c270d1887585e37902c7894e237bad8c2651f","last_reissued_at":"2026-05-18T00:16:08.403907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:08.403907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity estimates for nonlocal Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mouhamed Moustapha Fall","submitted_at":"2017-11-06T22:48:28Z","abstract_excerpt":"We prove H\\\"older regularity estimates up to the boundary for weak solutions $u$ to nonlocal Schr\\\"odinger equations subject to exterior Dirichlet conditions in an open set $\\Omega\\subset \\mathbb{R}^N$. The class of nonlocal operators considered here are defined, via Dirichlet forms, by kernels $K(x,y)$ bounded from above and below by $|x-y|^{N+2s}$, with $s\\in (0,1)$. The entries in the equations are in some Morrey spaces and the underline domain $\\Omega$ satisfies some mild regularity assumptions. In the particular case of the fractional Laplacian, our results are new. 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