Regularity for entropy solutions of parabolic p-Laplacian type equations
ISSN: 0214-1493
Any de publicació: 1999
Volum: 43
Número: 2
Pàgines: 665-683
Tipus: Article
Altres publicacions en: Publicacions matematiques
Resum
In this note we give some summability results for entropy solutions of the nonlinear parabolic equation $u_t -\operatorname{div} {\mathbf a}_p (x,\nabla u) = f$ in $]0,T[\times \Omega$ with initial datum in $L^1(\Omega)$ and assuming Dirichlet's boundary condition, where ${\mathbf a}_p(.,.)$ is a Carathéodory function satisfying the classical Leray-Lions hypotheses, $f\in L^1(]0,T[\times \Omega)$ and $\Omega$ is a domain in ${\mathbb R}^N$. We find spaces of type $L^r(0,T; {\cal M}^q(\Omega))$ containing the entropy solution and its gradient. We also include some summability results when $f = 0$ and the $p$-Laplacian equation is considered