Maximal L_p-regularity for x-dependent fractional heat equations with Dirichlet conditions

2023/12/04 by Abels, Helmut, Grubb, Gerd · 1 citation
#35R11 #35S16 #47G30 #60G52 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 35S15 #Secondary: 35K61

paper · doi:10.48550/arxiv.2312.01864

Abstract

We prove optimal regularity results in L_p-based function spaces in space and time for a large class of linear parabolic equations with a nonlocal elliptic operator in bounded domains with limited smoothness. Here the nonlocal operator is given by a strongly elliptic and even pseudodifferential operator of order 2a (0

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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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