L2-solvability of the dirichlet, neumann and regularity problems for parabolic equations with time-independent hölder-continuous coefficients

Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We establish the L2 -solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with time-independent Hölder-continuous diffusion coefficients on bounded Lipschitz domains in ℝn. This is achieved through the demonstration of invertibility of the relevant layer potentials, which is in turn based on Fredholm theory and a systematic transference scheme which yields suitable parabolic Rellich-type estimates.

Original languageEnglish
Pages (from-to)265-319
Number of pages55
JournalTransactions of the American Mathematical Society
Volume370
Issue number1
DOIs
Publication statusPublished - Jan 1 2018

Keywords

  • Boundary value problems
  • Layer potentials
  • Lipschitz domains
  • Parabolic equations
  • Rellich estimates

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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