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

Sascha Trostorff, Marcus Waurick

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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.
Original languageEnglish
JournalMathematische Nachrichten
Volume287
Issue number13
DOIs
Publication statusPublished - Sep 2014

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