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

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 unitary 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. DeGruyter, 2011]. The abstract framework is illustrated by various examples.