{"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 $N\\geq3$. 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 $p\\to2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04864","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}