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Article Dans Une Revue Analysis & PDE Année : 2020

On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgi-Nash-Moser regularity

Résumé

We study uniqueness of Dirichlet problems of second order divergence-form elliptic systems with transversally independent coefficients on the upper half-space in 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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Dates et versions

hal-01495944 , version 1 (27-03-2017)
hal-01495944 , version 2 (09-08-2021)

Identifiants

Citer

Pascal Auscher, Moritz Egert. On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgi-Nash-Moser regularity. Analysis & PDE, 2020, 13 (6), pp.1605-1632. ⟨10.2140/apde.2020.13.1605⟩. ⟨hal-01495944v2⟩
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