The Dirichlet problem for the biharmonic equation in a Lipschitz domain
Annales de l'Institut Fourier, Volume 36 (1986) no. 3, pp. 109-135.

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 (D), and the normal derivative is in L 2 (D). The resulting solution u takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of u is shown to be in L 2 (D).

Dans cet article nous étudions le problème de Dirichlet pour l’opérateur biharmonique Δ 2 , dans un domaine borné lipschitzien quelconque D dans R n , et nous donnons des bornes optimales. Nous démontrons des résultats d’existence et d’unicité quand les valeurs au bord ont des dérivées dans L 2 (D), et la dérivée normale appartient à L 2 (D). La solution qu’on obtient prend les valeurs au bord dans le sens de la convergence non-tangentielle, et la fonction maximale non-tangentielle de u appartient à L 2 (D).

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     author = {Dahlberg, Bj\"orn E. J. and Kenig, C. E. and Verchota, G. C.},
     title = {The {Dirichlet} problem for the biharmonic equation in a {Lipschitz} domain},
     journal = {Annales de l'Institut Fourier},
     pages = {109--135},
     publisher = {Institut Fourier},
     volume = {36},
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     year = {1986},
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}
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Dahlberg, Björn E. J.; Kenig, C. E.; Verchota, G. C. The Dirichlet problem for the biharmonic equation in a Lipschitz domain. Annales de l'Institut Fourier, Volume 36 (1986) no. 3, pp. 109-135. doi : 10.5802/aif.1062. http://archive.numdam.org/articles/10.5802/aif.1062/

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