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arXiv · 2204.04414

Lions' representation theorem and applications

Wolfgang Arendt·Isabelle Chalendar·Robert Eymard
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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.

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Wolfgang Arendt, Isabelle Chalendar, Robert Eymard. 2022-04-09. Lions' representation theorem and applications. https://arxiv.org/abs/2204.04414

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