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arXiv · 1809.09496

Unique continuation principles for a higher order fractional Laplace equation

Veronica Felli·Alberto Ferrero
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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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Veronica Felli, Alberto Ferrero. 2018-09-25. Unique continuation principles for a higher order fractional Laplace equation. https://arxiv.org/abs/1809.09496

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