Generalizations of the Lax-Milgram theorem

Details Generalizations of the Lax-Milgram theorem Generalizations of the Lax-Milgram theorem

2008-05-30

arxiv.org/abs/0805.4710v1

Boundary Value Problems Volume 2007 (2007), Article ID 87104

Mathematics

Functional Analysis

Scientific paper

10.1155/2007/87104

We prove a linear and a nonlinear generalization of the Lax-Milgram theorem.
In particular we give sufficient conditions for a real-valued function defined
on the product of a reflexive Banach space and a normed space to represent all
bounded linear functionals of the latter. We also give two applications to
singular differential equations.

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