Regular points for elliptic equations with discontinuous coefficients

W. Littman; G. Stampacchia; H. F. Weinberger

Displaying similar documents to “Regular points for elliptic equations with discontinuous coefficients”

The $L_{p}$ approach to the Dirichlet problem. Part I : regularity theorems

Shmuel Agmon (1959)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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 $\sum_{i, j} D_{x_{i}} (a_{i j} (x) D_{x_{j}}), where λ w (x) | ξ |^{2} \leq \sum_{i, j} a_{i j} (x) ξ_{i} ξ_{j} \leq Λ w (x) | ξ |^{2} .$ 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 $w$ .

On elliptic partial differential equations

L. Nirenberg (1959)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Nonequivalence of regular boundary points for the Laplace and nondivergence equations, even with continuous coefficients

Keith Miller (1970)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Linear elliptic operators with measurable coefficients

Neil S. Trudinger (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Displaying similar documents to “Regular points for elliptic equations with discontinuous coefficients”

The L p approach to the Dirichlet problem. Part I : regularity theorems

The Wiener test for degenerate elliptic equations

On elliptic partial differential equations

Nonequivalence of regular boundary points for the Laplace and nondivergence equations, even with continuous coefficients

Linear elliptic operators with measurable coefficients

The $L_{p}$ approach to the Dirichlet problem. Part I : regularity theorems