A change of variable for Dahlberg-Kenig-Pipher operators

In the present article, we give a method to deal with Dahlberg-Kenig-Pipher (DPK) operators in boundary value problems on the upper half plane. We give a nice subclass of the weak DKP operators that generates the full class of weak DKP operators under the action of bi-Lipschitz changes of variable o...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2022-08, Vol.150 (8), p.3565-3579
1. Verfasser: Feneuil, Joseph
Format: Artikel
Sprache:eng
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Zusammenfassung:In the present article, we give a method to deal with Dahlberg-Kenig-Pipher (DPK) operators in boundary value problems on the upper half plane. We give a nice subclass of the weak DKP operators that generates the full class of weak DKP operators under the action of bi-Lipschitz changes of variable on \mathbb {R}^n_+ that fix the boundary \mathbb {R}^{n-1}. Therefore, if one wants to prove a property on DKP operators which is stable by bi-Lipschitz transformations, one can directly assume that the operator belongs to the subclass. Our method gives an alternative proof to some past results and self-improves others beyond the existing literature.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/15923