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The Wiener test for degenerate elliptic equations

E. B. FabesD. S. JerisonC. E. Kenig — 1982

Annales de l'institut Fourier

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 .

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