Boundary value problems for elliptic equations.

Carlos E. Kenig

Displaying similar documents to “Boundary value problems for elliptic equations.”

The Dirichlet problem for elliptic equations with drift terms.

Carlos E. Kenig, Jill Pipher (2001)

Publicacions Matemàtiques

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We establish absolute continuity of the elliptic measure associated to certain second order elliptic equations in either divergence or nondivergence form, with drift terms, under minimal smoothness assumptions on the coefficients.

Fatou theorems for some nonlinear elliptic equations.

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

Revista Matemática Iberoamericana

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Area integral estimates for higher order elliptic equations and systems

Björn E. J. Dahlberg, Carlos E. Kenig, Jill Pipher, G. C. Verchota (1997)

Annales de l'institut Fourier

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Let $L$ be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in $L^{p}$ norm between the maximal function and the square function of solutions to $L$ in Lipschitz domains. Several applications of this result are discussed.

A note on the Rellich formula in Lipschitz domains.

Alano Ancona (1998)

Publicacions Matemàtiques

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Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain Ω of R and having Lipschitz coefficients in Ω. It is shown that the Rellich formula with respect to Ω and L extends to all functions in the domain D = {u ∈ H (Ω); L(u) ∈ L(Ω)} of L. This answers a question of A. Chaïra and G. Lebeau.

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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An endpoint Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains.

Pascal Auscher, Philippe Tchamitchian (1999)

Publicacions Matemàtiques

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We prove a commutator inequality of Littlewood-Paley type between partial derivatives and functions of the Laplacian on a Lipschitz domain which gives interior energy estimates for some BVP. It can be seen as an endpoint inequality for a family of energy estimates.

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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Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

Mikhail Borsuk (1998)

Annales Polonici Mathematici

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We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives.

Oblique derivative problems for the laplacian in Lipschitz domains.

Jill Pipher (1987)

Revista Matemática Iberoamericana

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The aim of this paper is to extend the results of Calderón [1] and Kenig-Pipher [12] on solutions to the oblique derivative problem to the case where the data is assumed to be BMO or Hölder continuous.