On uniqueness results for Dirichlet problems of elliptic systems without de Giorgi–Nash–Moser regularity

Pascal Auscher, Moritz Egert

Type: Article

Publication Date: 2020-09-12

Citations: 10

DOI: https://doi.org/10.2140/apde.2020.13.1605

Abstract

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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+ PDF Chat	On the L p -Poisson Semigroup Associated with Elliptic Systems	2017	José María Martell Dorina Mitrea Irina Mitrea Marius Mitrea
+	Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems	1994	Carlos E. Kenig
+ PDF Chat	Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients	2016	Ariel Barton
+ PDF Chat	A priori estimates for boundary value elliptic problems via first order systems	2016	Pascal Auscher Sebastian Stahlhut
+ PDF Chat	The method of layer potentials in<i>L<sup>p</sup></i>and endpoint spaces for elliptic operators with<i>L<sup>∞</sup></i>coefficients	2015	Steve Hofmann Marius Mitrea Andrew J. Morris
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