Unique Continuation for Fractional Orders of Elliptic Equations

By Hui Yu. 2016

50 citations recorded by the source corpus.

We establish the strong unique continuation property of fractional orders of linear elliptic equations with Lipschitz coefficients by establishing almost monotonicity for an Almgren-type frequency functional via an extension procedure.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9d0a1153dd38e37942d81b0ffdcab391734380ca

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

The fractional Calderón problem: Low regularity and stability (2017, background): “[Yu17] H. Yu, Unique continuation for fractional orders of elliptic equations, Annals of PDE, 3(2), 2017, 16.”
The Calderón problem for variable coefficients nonlocal elliptic operators (2017, methodology): “9) were proved in [46, 51], so we skip the details.”
Fractional thoughts (2017, methodology): “We also mention the recent paper [Yu17] in which the author uses a generalization of the monotonicity formula in Theorem 14.”
The Calderón problem for the fractional Schrödinger equation (2016, background): “2 is classical [Riesz 1938] at least with stronger conditions on u, and even the strong unique continuation principle holds in this context [Fall and Felli 2014; Rüland 2015; Yu 2017].”
Quantitative approximation properties for the fractional heat equation (2017, background): “Section 6 in [35] or also [40] for weak and strong unique continuation properties of the variable coefficient fractional Laplacian and the associated necessary regularity assumptions on the coefficients).”