A change of variable for Dahlberg-Kenig-Pipher operators

Feneuil, Joseph

doi:10.1090/proc/15923

A change of variable for Dahlberg-Kenig-Pipher operators
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Proc. Amer. Math. Soc. 150 (2022), 3565-3579 Request permission

Abstract:

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.

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