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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 2, 1997, pp. 281–309
DOI: 10.4171/ZAA/764

Published online: 1997-06-30

Asymptotic Behaviour of Relaxed Dirichiet Problems Involving a Dirichlet-Poincar Form

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

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

We study the convergence of the solutions of a sequence of relaxed Dirichlet prob lems relative to Dirichlet forms to the solution of the Γ-limit problem. In particular we prove the strong convergence in $D^P_0[a,Ω](1≤p≤2)$ and the existence of "correctors" for the strong convergence in $D0[a,Ω]$. The above two results are generalizations to our framework of previous results proved in [10] in the usual uniformly elliptic setting.

Keywords: $\Gamma$-convergence, Dirichlet forms, subelliptic equations

Biroli Marco, Tchou N.: Asymptotic Behaviour of Relaxed Dirichiet Problems Involving a Dirichlet-Poincar Form. Z. Anal. Anwend. 16 (1997), 281-309. doi: 10.4171/ZAA/764