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

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. Savaré (1998) about the regularity issue of the Laplace equation.

This work is part of the second author's ongoing Ph.D. research, which is carried out at Moulay Ismail University, Meknes-Morocco. arXiv admin note: text overlap with arXiv:1707.03013