Based on a variant of the frequency function approach of Almgren, we establish an optimal upper bound on the vanishing order of solutions to variable coefficient Schrödinger equations at a portion of the boundary of a domain. Such bound provides a quantitative form of strong unique continuation at the boundary. It can be thought of as a boundary analogue of an interior result recently obtained by Bakri and Zhu for the standard Laplacian.
Quantitative uniqueness for elliptic equations at the boundary of C1,Dini domains
GAROFALO, NICOLA
2016
Abstract
Based on a variant of the frequency function approach of Almgren, we establish an optimal upper bound on the vanishing order of solutions to variable coefficient Schrödinger equations at a portion of the boundary of a domain. Such bound provides a quantitative form of strong unique continuation at the boundary. It can be thought of as a boundary analogue of an interior result recently obtained by Bakri and Zhu for the standard Laplacian.
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