Lions' representation theorem and applications
Functional Analysis
2022-04-12 v1
Abstract
The Representation Theorem of Lions (RTL) is a version of the Lax--Milgram Theorem where completeness of one of the spaces is not complete. In this paper, RTL is deduced from an operator-theoretical version on normed space. The main point of the paper is a theory of derivations, based on RTL, for which well-posedness is proved. One application concerns non-autonomous evolution equations with a new initial-value and a periodic boundary condition for the time variable.
Cite
@article{arxiv.2204.04414,
title = {Lions' representation theorem and applications},
author = {Wolfgang Arendt and Isabelle Chalendar and Robert Eymard},
journal= {arXiv preprint arXiv:2204.04414},
year = {2022}
}