Unique continuation principles for a higher order fractional Laplace equation

2018/09/25 by Felli, Veronica, Ferrero, Alberto · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.09496

Abstract

In this paper we prove strong unique continuation principle and unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the Caffarelli-Silvestre extension method combined with an Almgren type monotonicity formula. The corresponding extended problem is formulated as a systems of two second order equations with singular or degenerate weights in a half-space, for which asymptotics estimates are derived by a blow-up analysis.

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• The higher-order fractional Schrödinger equation with nonlinear local perturbations: Uniqueness
• On a class of thin obstacle-type problems for the bi-Laplacian operator

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