Abstract
In this paper, we investigate divergence-form linear elliptic systems on bounded Lipschitz domains in \(\mathbb {R}^{d+1}, d \ge 2\), with L 2 boundary data. The coefficients are assumed to be real, bounded, and measurable. We show that when the coefficients are small, in Carleson norm, compared to one that is continuous on the boundary, we obtain solvability for both the Dirichlet and regularity boundary value problems given that the coefficients satisfy a certain “pseudo-symmetry” condition.
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This paper culminated from my thesis work at The University of Chicago. I would like to thank Professor Carlos E. Kenig for being the most patient, supportive, and helpful advisor. Without him, this project would not have been possible.
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Nguyen, N.T. The Dirichlet and Regularity Problems for Some Second Order Linear Elliptic Systems on Bounded Lipschitz Domains. Potential Anal 45, 167–186 (2016). https://doi.org/10.1007/s11118-016-9542-5
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DOI: https://doi.org/10.1007/s11118-016-9542-5