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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Ding Hua (1989)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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 , on an arbitrary bounded Lipschitz domain in . We establish existence and uniqueness results when the boundary values have first derivatives in , and the normal derivative is in . The resulting solution takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of is shown to be in .
Carlos E. Kenig (1984-1985)
Séminaire Équations aux dérivées partielles (Polytechnique)
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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.
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.
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.
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....
Björn E.J. Dahlberg (1979)
Mathematica Scandinavica
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Björn Dahlbert (1979)
Studia Mathematica
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