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- Title
A note on elliptic type boundary value problems with maximal monotone relations.
- Authors
Trostorff, Sascha; Waurick, Marcus
- 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.
- Subjects
BOUNDARY value problems; HILBERT space; DIFFERENTIAL-algebraic equations; GELFAND-Naimark theorem; DIFFERENTIAL equations; COMPLEX variables
- Publication
Mathematische Nachrichten, 2014, Vol 287, Issue 13, p1545
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.201200242