Lions' representation theorem and applications

DOI10.1016/J.JMAA.2022.126946zbMath1510.35166arXiv2204.04414WikidataQ123188651 ScholiaQ123188651MaRDI QIDQ6396088

Isabelle Chalendar, Robert Eymard, Wolfgang Arendt

Publication date: 9 April 2022

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.

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Linear accretive operators, dissipative operators, etc. (47B44)

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