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We establish interior gradient estimates in weighted Morrey spaces for weak solutions $u$ to the equation under a small BMO condition in $x$ for $\\A$. As a consequence, we obtain that $\\nabla u$ is in the classical Morrey space $\\calM^{q,\\lambda}$ or weighted space $L^q_w$ whenever $|\\F|^{\\frac{1}{p-1}}$ is respectively in $"},"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":"1810.12496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-30T02:43:25Z","cross_cats_sorted":[],"title_canon_sha256":"09276da23b29dd2f9f672e95c0c6b95b0f486bc66420bf0cdf0fda3a03bd25d2","abstract_canon_sha256":"af0ed8fe990fe86acac9b79972322691fc8294237ff2e5e6e3ce7247c73052a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:56.935632Z","signature_b64":"uJhWXcaaEGqF8FqDtwfFvo0nrsPNepv1+q9G7iUKTQ/ojV6gloFalAMcMsVUje8Hdg/EAr71gw78ZjASbSa1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f238743fc0dc8a1b351dfdecdd881b4a430985a2ad4e84dee843e9ac0e518ea","last_reissued_at":"2026-05-18T00:01:56.935019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:56.935019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Di Fazio, Truyen Nguyen","submitted_at":"2018-10-30T02:43:25Z","abstract_excerpt":"We study regularity for solutions of quasilinear elliptic equations of the form $\\div \\A(x,u,\\nabla u) = \\div \\F $ in bounded domains in $\\R^n$. 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