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arXiv · 1803.07550

Riesz bases for $L^2(\partial \Omega)$ and regularity for the Laplace equation in Lipschitz domains

Abdellatif Chaira·Soumia Touhami
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Abstract

In a paper from 1996, D. Jerison and C. Kenig among other results provided a $H^{1/2}$ regularity result for the Dirichlet problem for the Laplace equation in Lipschitz domains. In this article, we adopt a Hilbertian approach to construct two Riesz bases for $L^2(\partial \Omega),$ which will allow to find in a different way some of the results of D. Jerison and C. Kenig, and G. Savar\'{e} (1998) about the regularity issue of the Laplace equation.

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Abdellatif Chaira, Soumia Touhami. 2018-03-20. Riesz bases for $L^2(\partial \Omega)$ and regularity for the Laplace equation in Lipschitz domains. https://arxiv.org/abs/1803.07550

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