WIAS Preprint No. 2097, (2015)

Hölder estimates for parabolic operators on domains with rough boundary



Authors

  • Disser, Karoline
  • Rehberg, Joachim
  • ter Elst, A. F. M.

2010 Mathematics Subject Classification

  • 35K20 35B45 35B65 35B05

Keywords

  • Parabolic initial boundary value problems, Hölder continuity

DOI

10.20347/WIAS.PREPRINT.2097

Abstract

In this paper we investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain -- including a very weak compatibility condition between the Dirichlet boundary part and its complement -- we prove Hölder continuity of the solution in space and time.

Appeared in

  • Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), XVII (2017), pp. 65--79.

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