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

作者：Trostorff Sascha^*; Waurick Marcus

来源：Mathematische Nachrichten, 2014, 287(13): 1545-1558.

DOI：10.1002/mana.201200242

• Elliptic differential equations in divergence form
• maximal monotone relations
• Gelfand triples

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.

• 出版日期2014-9