Higher regularity of solutions to the singular p-Laplacean parabolic\n system

2012/09/05 by Francesca Crispo, Paolo Maremonti, Crispo, Francesca +1 · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1209.1038

Abstract

We study existence and regularity properties of solutions to the singular\np-Laplacean parabolic system in a bounded domain \Ω. The main purpose\nis to prove global L^r(\ε,T;L^q(\Ω)), \ε\≥0,\nintegrability properties of the second spatial derivatives and of the time\nderivative of the solutions. Hence, for suitable p and exponents r, ,q, by\nSobolev embedding theorems, we deduce global regularity of u and \∇ u\nin H "older spaces. Finally we prove a global pointwise bound for the solution\nunder the assumption p>\(2n)/(n+2).\n

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• Existence of global weak solutions to a parabolic p-Laplacian problem with convective term

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