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

Sascha Trostorff, Marcus Waurick

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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.
Original languageEnglish
Pages (from-to)1545-1558
Number of pages14
JournalMathematische Nachrichten
Issue number13
Early online date17 Apr 2014
Publication statusPublished - 30 Sep 2014


  • Hilbert space
  • boundary value problem
  • maximal monotone

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