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Relaxation for Dirichlet Problems Involving a Dirichlet Form

Name: Relaxation for Dirichlet Problems Involving a Dirichlet Form
Keywords: Dirichlet forms, Variational methods applied to PDEs, Asymptotic behavior of solutions to PDEs, asymptotic behaviour, positive Borel measures, Dirichlet form, Dirichlet spaces

Relaxation for Dirichlet problems involving a Dirichlet form

descriptionPublicationkeyboard_double_arrow_right Article 31 Mar 2000 Italy Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Zeitschrift für Analysis und ihre Anwendungen, volume 19, pages 203-225 (issn: 0232-2064, eissn: 1661-4534,

Authors: BIROLI, MARCO; TCHOU N.;

doi: 10.4171/zaa/946

handle: 11311/527388 , 11311/527317

Relaxation for Dirichlet Problems Involving a Dirichlet Form

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Abstract

For a fixed Dirichlet form, we study the space of positive Borel measures (possibly infinite) which do not charge polar sets. We prove the density in this space of the set of the measures which represent varying, domains. Our method is constructive. For the Laplace operator, the proof was based on a pavage of the space. Here, we substitute this notion by that of homogeneous covering in the sense of Coiffman and Weiss.

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Italy

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Keywords

Dirichlet forms, Variational methods applied to PDEs, Asymptotic behavior of solutions to PDEs, asymptotic behaviour, positive Borel measures, Dirichlet form, Dirichlet spaces

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