A note on elliptic type boundary value problems with maximal monotone relations

Sascha Trostorff, Marcus Waurick

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as “coefficients”. A reformulation of the respective problems is constructed such that they turn out to be unitarily equivalent to inverting a maximal monotone relation in a Hilbert space. The method is based on the idea of “tailor-made” distributions as provided by the construction of extrapolation spaces, see e.g. [Picard, McGhee: Partial Differential Equations: A unified Hilbert Space Approach (De Gruyter, 2011)]. The abstract framework is illustrated by various examples.
LanguageEnglish
Pages1545-1558
Number of pages14
JournalMathematische Nachrichten
Volume287
Issue number13
Early online date17 Apr 2014
DOIs
Publication statusPublished - 30 Sep 2014

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Monotone
Hilbert space
Boundary Value Problem
Reformulation
Extrapolation
Divergence
Partial differential equation
Coefficient
Framework
Form
Standards

Keywords

  • Hilbert space
  • boundary value problem
  • maximal monotone

Cite this

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A note on elliptic type boundary value problems with maximal monotone relations. / Trostorff, Sascha; Waurick, Marcus.

In: Mathematische Nachrichten, Vol. 287, No. 13, 30.09.2014, p. 1545-1558.

Research output: Contribution to journalArticle

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