Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2000-03-31
Relaxation for Dirichlet Problems Involving a Dirichlet FormMarco Biroli and N. Tchou (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