On fractional p-laplacian parabolic problem with general data

2016/12/05 by Abdellaoui, Boumediene, Attar, Ahmed, Bentifour, Rachid +1 · 2 citations
#35B09 #35K59 #35K65 #35K67 #35K92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.01301

Abstract

In this article the problem to be studied is the following (P) \ u_t+(-\D^s_p) u · amp; = · amp; f(x,t) · amp; in Ø_T≡ Ω× (0,T),
u · amp; = · amp; 0 · amp; in (\ren∖Ø) × (0,T),
u · amp; ≥ · amp; 0 · amp; in \ren × (0,T),
u(x,0) · amp; = · amp; u₀(x) · amp; in Ø,% . where Ω is a bounded domain, and (-\D^s_p) is the fractional p-Laplacian operator defined by (-\D^s_p) u(x,t):=P.V∫_\ren \dfrac|u(x,t)-u(y,t)|^p-2(u(x,t)-u(y,t))|x-y|^N+ps dy with 1

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• Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems

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