Maximal regularity with weights for parabolic problems with inhomogeneous boundary conditions

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Abstract

In this paper, we establish weighted Lq–Lp-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in time and in space, and yield flexibility in the optimal regularity of the initial-boundary data and allow to avoid compatibility conditions at the boundary. The novelty of the followed approach is the use of weighted anisotropic mixed-norm Banach space-valued function spaces of Sobolev, Bessel potential, Triebel–Lizorkin and Besov type, whose trace theory is also subject of study.

Original languageEnglish
Pages (from-to)1-50
Number of pages50
JournalJournal of Evolution Equations
DOIs
Publication statusE-pub ahead of print - 2019

Keywords

  • Anisotropic spaces
  • Besov
  • Bessel potential
  • Inhomogeneous boundary conditions
  • Maximal regularity
  • Mixed-norms
  • Parabolic initial-boundary value problems
  • Sobolev
  • Traces
  • Triebel–Lizorkin
  • Vector-valued
  • Weights

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