Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains

Carlos E. Kenig

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Displaying similar documents to “Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains”

A regularity result for boundary value problems on Lipschitz domains

Ding Hua (1989)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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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 $L^{2} (\partial D)$ .

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.

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.

Boundary value problems in Lipschitz cylinders for three-dimensional parabolic systems.

Russell M. Brown, Zhongwei Shen (1992)

Revista Matemática Iberoamericana

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We consider initial-boundary value problems for a parabolic system in a Lipschitz cylinder. When the space dimension is three, we obtain estimates for the solutions when the lateral data taken from the best possible range of L-spaces.

Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.

Hans Triebel (2002)

Revista Matemática Complutense

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Function spaces of type B and F cover as special cases classical and fractional Sobolev spaces, classical Besov spaces, Hölder-Zygmund spaces and inhomogeneous Hardy spaces. In the last 2 or 3 decades they haven been studied preferably on R and in smooth bounded domains in R including numerous applications to pseudodifferential operators, elliptic boundary value problems etc. To a lesser extent spaces of this type have been considered in Lipschitz domains....

L...-estimates for Green potentials in Lipschitz domains.

Björn E.J. Dahlberg (1979)

Mathematica Scandinavica

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

Björn Dahlbert (1979)

Studia Mathematica

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