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On uniqueness results
for Dirichlet problems of elliptic systems without de
Giorgi–Nash–Moser regularity
Pascal Auscher and Moritz Egert |
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Vol. 13 (2020), No. 6, 1605–1632
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Abstract |
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We study uniqueness of Dirichlet problems of second-order divergence-form elliptic systems with transversally independent coefficients on the upper half-space in the absence of regularity of solutions. To this end, we develop a substitute for the fundamental solution used to invert elliptic operators on the whole space by means of a representation via abstract single-layer potentials. We also show that such layer potentials are uniquely determined. |
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Keywords
Dirichlet problems, uniqueness of solutions, elliptic
systems, single-layer operators
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Mathematical Subject Classification 2010
Primary: 35J57, 35A02
Secondary: 35J50, 42B25, 35C15
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Milestones
Received: 28 March 2017
Accepted: 13 August 2019
Published: 12 September 2020
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Authors |
| Pascal Auscher | |
| Université Paris-Saclay CNRS Laboratoire de Mathématiques d’Orsay Orsay France |
Laboratoire Amiénois de Mathématique
Fondamentale et Appliquée CNRS-UMR 7352 Université de Picardie-Jules Verne Amiens France |
| Moritz Egert | |
| Université Paris-Saclay CNRS Laboratoire de Mathématiques d’Orsay Orsay France |
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