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A note on elliptic type boundary value problems with maximal monotone relations
Author(s) -
Trostorff Sascha,
Waurick Marcus
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200242
Subject(s) - mathematics , monotone polygon , hilbert space , divergence (linguistics) , type (biology) , boundary value problem , pure mathematics , extrapolation , space (punctuation) , strongly monotone , mathematical analysis , relation (database) , geometry , ecology , philosophy , linguistics , database , computer science , biology
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.