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In this paper we are interested in the $W^{2,2}$ regularity of the weak solutions of elliptic equations of the type \\begin{align}\\label{Probelma in abstract} \\lambda u-L_{\\nu,\\Omega} u=f, \\end{align} where $\\lambda>0$, $f\\in L^2(\\Omega,\\nu)$ and $L_{\\nu,\\Omega}$ is the self-adjo"},"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":"1609.07337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T12:32:24Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"97bc0cdcb75bdd07c7568ce1102e45a632361b73d2ac54b087dbbe78bccfe681","abstract_canon_sha256":"0de598fc53db63e3843869e6b816f23ae4d6a2a3f9f6786ec83e72a406aaf051"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:46:56.495604Z","signature_b64":"BgNi+AsRfvaKhnrmITimxlPLA0Pofk4YW+OO/iV6Cq7F7Ky23MSm/6BYO2vzXbTnMfqt2PRf/HzFNnc7ihGfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42ec84cf13efb5343ed67b87a0d9f0cf5380230748c6ac1554b496577ddc4dd2","last_reissued_at":"2026-07-05T02:46:56.495174Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:46:56.495174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal Sobolev regularity for solutions of elliptic equations in Banach spaces endowed with a weighted Gaussian measure: the convex subset case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"G. 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