EMIS ELibM Electronic Journals Zeitschrift für Analysis und ihre Anwendungen
Vol. 19, No. 1, pp. 203-225 (2000)

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Relaxation for Dirichlet Problems Involving a Dirichlet Form

M. Biroli and N. Tchou

Politecnico di Milano, Dept. Math., Piazza L. da Vinci 32, 20133 Milano, Italy Université de Rennes 1, IRMAR, Beaulieu, 35042 Rennes Cedex, France

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 {\it homogeneous covering} in the sense of Coiffman and Weiss.

Keywords: dirichlet spaces, Asymptotic behavior, Variational methods

Classification (MSC2000): 31C25, 35B40, 35A15

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Electronic fulltext finalized on: 25 Jul 2001. This page was last modified: 9 Nov 2001.

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