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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Accretive mappings
verfasst von : Tomáš Roubíček
Erschienen in: Nonlinear Partial Differential Equations with Applications
Verlag: Springer Basel
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Besides bounded mappings from a Sobolev space to its dual, there is an alternative understanding of differential operators as unbounded operators from a (typically dense) subset of a function space to itself. This calls for a generalization of a monotonicity concept for mappings
D
→
X
, with
X
a Banach space and
D
its subset. Moreover,
X
need not be reflexive because the weak-compactness arguments will be replaced by metric properties and completeness. The main benefit from this approach will be achieved for evolution problems in Chapter 9 but the method is of some interest in steady-state problems themselves.