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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 1, 2000, pp. 203–225
DOI: 10.4171/ZAA/946

Published online: 2000-03-31

Relaxation for Dirichlet Problems Involving a Dirichlet Form

Marco Biroli[1] and N. Tchou[2]

(1) Politecnico di Milano, Italy
(2) Université de Rennes I, France

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.

Keywords: Dirichiet spaces, asymptotic behavior, variational methods

Biroli Marco, Tchou N.: Relaxation for Dirichlet Problems Involving a Dirichlet Form. Z. Anal. Anwend. 19 (2000), 203-225. doi: 10.4171/ZAA/946