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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Carlos E. Kenig (1983-1984)
Séminaire Équations aux dérivées partielles (Polytechnique)
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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.
Carlos E. Kenig (1984-1985)
Séminaire Équations aux dérivées partielles (Polytechnique)
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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 .
Ding Hua (1989)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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.
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.
Carlos E. Kenig (1991)
Publicacions Matemàtiques
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In this note I will describe some recent results, obtained jointly with R. Fefferman and J. Pipher [RF-K-P], on the Dirichlet problem for second-order, divergence form elliptic equations, and some work in progress with J. Pipher [K-P] on the corresponding results for the Neumann and regularity problems.