A note on the Rellich formula in Lipschitz domains.

Alano Ancona

Displaying similar documents to “A note on the Rellich formula in Lipschitz domains.”

Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains

Jang-Mei G. Wu (1978)

Annales de l'institut Fourier

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On a Lipschitz domain $D$ in $R^{n}$ , three theorems on harmonic functions are proved. The first (boundary Harnack principle) compares two positive harmonic functions at interior points near an open subset of the boundary where both functions vanish. The second extends some familiar geometric facts about the Poisson kernel on a sphere to the Poisson kernel on $D$ . The third theorem, on non-tangential limits of quotient of two positive harmonic functions in $D$ , generalizes Doob’s relative Fatou...

On the Poisson integral for Lipschitz and $C^{1}$ -domains

Björn Dahlbert (1979)

Studia Mathematica

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Fatou theorems for some nonlinear elliptic equations.

Eugene Fabes, Nicola Garofalo, Santiago Marin Malave, Sandro Salsa (1988)

Revista Matemática Iberoamericana

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Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains

Carlos E. Kenig (1983-1984)

Séminaire Équations aux dérivées partielles (Polytechnique)

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The Dirichlet problem for the biharmonic equation in a Lipschitz domain

Carlos E. Kenig (1984-1985)

Séminaire Équations aux dérivées partielles (Polytechnique)

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The Dirichlet problem for the biharmonic equation in a Lipschitz domain

Björn E. J. Dahlberg, C. E. Kenig, G. C. Verchota (1986)

Annales de l'institut Fourier

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In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator $Δ^{2}$ , on an arbitrary bounded Lipschitz domain $D$ in $R^{n}$ . We establish existence and uniqueness results when the boundary values have first derivatives in $L^{2} (\partial D)$ , and the normal derivative is in $L^{2} (\partial D)$ . The resulting solution $u$ takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of $\nabla u$ is shown to be in $L^{2} (\partial D)$ .

Boundary behaviour of positive harmonic functions on Lipschitz domains.

Carroll, Tom (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

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Boundary integral methods for harmonic differential forms in Lipschitz domains.

Mitrea, Dorina, Mitrea, Marius (1996)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Convex domains and unique continuation at the boundary.

Vilhelm Adolfsson, Luis Escauriaza, Carlos Kenig (1995)

Revista Matemática Iberoamericana

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We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.