The Dirichlet problem for standard weighted Laplacians in the upper half plane

Marcus Carlsson, Jens Wittsten

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)

Abstract

In this paper the Dirichlet problem for a class of standard weighted Laplace operators in the upper half plane is solved by means of a counterpart of the classical Poisson integral formula. Boundary limits and representations of the associated solutions are studied within a framework of weighted spaces of distributions. Special attention is given to the development of a, suitable uniqueness theory for the Dirichlet problem under appropriate growth constraints at infinity. (C) 2015 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)868-889
JournalJournal of Mathematical Analysis and Applications
Volume436
Issue number2
DOIs
Publication statusPublished - 2016

Subject classification (UKÄ)

  • Mathematical Analysis

Keywords

  • Poisson integral
  • Weighted Laplace operator
  • Poisson kernel
  • Weighted
  • space of distributions

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