Displaying similar documents to “On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes”

The p -Laplacian in domains with small random holes

M. Balzano, T. Durante (2003)

Bollettino dell'Unione Matematica Italiana

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P h {ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . where 2 p n and E h are random subsets of a bounded open set D of R n n 2 . By means of a variational approach, we study the asymptotic behaviour of solutions of P h , characterizing the limit problem for suitable sequences of random sets.

The Wiener test for degenerate elliptic equations

E. B. Fabes, D. S. Jerison, C. E. Kenig (1982)

Annales de l'institut Fourier

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We consider degenerated elliptic equations of the form i , j D x i ( a i j ( x ) D x j ) , where λ w ( x ) | ξ | 2 i , j a i j ( x ) ξ i ξ j Λ w ( x ) | ξ | 2 . Under suitable assumptions on w , we obtain a characterization of Wiener type (involving weighted capacities) for the set of regular points for these operators. The set of regular points is shown to depend only on w . The main tool we use is an estimate for the Green function in terms of w .