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We show that the bounded weak solutions are locally continuous in the range $$2-\\epsilon_0\\leq p<2,$$ provided $\\epsilon_0>0$ is small enough, and the continuity is stable as $p\\to2$."},"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":"1812.04864","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-12T09:42:32Z","cross_cats_sorted":[],"title_canon_sha256":"cedd837f87c75fd029732b5dac50f549e6011a32c9c865661453d2ab9cbc8439","abstract_canon_sha256":"a587a9c21d46f403708bf7ce67f79ee6b66f7b6e17644fbb066af7fe8031ca45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:20.483472Z","signature_b64":"V+fn+VbY2q5OuLlHeG6ZxddV5WXX8ko6AYEbVRpBt6FYYFiLmyOmuHWI7elN56CJ9oXXwUQtlOGmtAc/YOzeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3849d1fe298134352262c5d4b581b616e7a39843f19a55a4c91c6686273f2934","last_reissued_at":"2026-05-17T23:58:20.482943Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:20.482943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the continuity of solutions to doubly singular parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qifan Li","submitted_at":"2018-12-12T09:42:32Z","abstract_excerpt":"This paper considers a certain doubly singular parabolic equations with one singularity occurs in the time derivative, whose model is \\begin{equation*} \\partial_t\\beta(u)-\\operatorname{div}|Du|^{p-2}Du\\ni0,\\qquad \\text{in}\\quad \\Omega\\times(0,T)\\end{equation*} where $\\Omega\\subset\\mathbb{R}^N$ and $N\\geq3$. 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