Fabes, Jerison, Kenig: The Wiener test for degenerate elliptic equations

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E. B. Fabes; D. S. Jerison; C. E. Kenig
The Wiener test for degenerate elliptic equations
Annales de l'institut Fourier, 32 no. 3 (1982), p. 151-182, doi: 10.5802/aif.883
Article PDF | Reviews MR 84g:35067 | Zbl 0488.35034 | 1 citation in Cedram

Résumé - Abstract

We consider degenerated elliptic equations of the form

$$\sum _{i,j} D_{x_i}(a_{ij}(x) D_{x_j}), \text{where} \lambda w(x) |\xi |^2 \le \sum _{i,j} a_{ij} (x) \xi _i\xi _j \le \Lambda w(x) |\xi |^2.$$

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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