{"paper":{"title":"Parabolic equation in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Zatorska-Goldstein, Iwona Chlebicka, Piotr Gwiazda","submitted_at":"2018-06-15T11:03:19Z","abstract_excerpt":"We study a general nonlinear parabolic equation on a Lipschitz bounded domain in $\\mathbb{R}^N$, \\begin{equation*} \\left\\{\\begin{array}{l l} \\partial_t u-\\mathrm{div} A(t,x,\\nabla u)= f(t,x)&\\text{in}\\ \\ \\Omega_T,\\\\ u(t,x)=0 &\\ \\mathrm{ on} \\ (0,T)\\times\\partial\\Omega,\\\\ u(0,x)=u_0(x)&\\text{in}\\ \\Omega, \\end{array}\\right. \\end{equation*} with $f\\in L^\\infty(\\Omega_T)$ and $u_0\\in L^\\infty(\\Omega)$. The growth of the monotone vector field $A$ is controlled by a generalized fully anisotropic $N$-function $M:[0,T)\\times\\Omega\\times\\mathbb{R}^N\\to[0,\\infty)$ inhomogeneous in time and space, and un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06711","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"}