Diego Marcon, Rafayel Teymurazyan
Published 2020-01-05Version 1
We study a free boundary optimization problem for the fractional Laplacian with a volume constraint and a lower bound. We prove existence and optimal H\"{o}lder regularity of solutions, as well as derive geometric properties of solutions and of the corresponding exterior free boundary.
Analytic regularity of a free boundary problem
A free boundary optimization problem for the $\infty$-Laplacian
The influence of fractional diffusion in Fisher-KPP equations
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