A regularity result for boundary value problems on Lipschitz domains

Ding Hua

Displaying similar documents to “A regularity result for boundary value problems on Lipschitz domains”

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

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.

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....

The Trace of Sobolev-Slobodeckij spaces on Lipschitz domains.

Jürgen Marschall (1987)

Manuscripta mathematica

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Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.

Gary M. Lieberman (1988)

Journal für die reine und angewandte Mathematik

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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.

Doubling properties and unique continuation at the boundary for elliptic operators with singular magnetic fields

Xiangxing Tao (2002)

Studia Mathematica

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Let u be a solution to a second order elliptic equation with singular magnetic fields, vanishing continuously on an open subset Γ of the boundary of a Lipschitz domain. An elementary proof of the doubling property for u² over balls centered at some points near Γ is presented. Moreover, we get the unique continuation at the boundary of Dini domains for elliptic operators.