Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 211, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2021.112473
Keywords
Free boundary problems; Global solutions; Obstacle problem
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This paper provides a full classification of global solutions of the obstacle problem for the fractional Laplacian with compact coincidence set and at most polynomial growth in dimension N >= 3, and establishes a bijection onto a set of polynomials describing the asymptotics of the solution. Additionally, it is proven that coincidence sets of global solutions that are compact are also convex if the solution has at most quadratic growth.
In this paper we give a full classification of global solutions of the obstacle problem for the fractional Laplacian (including the thin obstacle problem) with compact coincidence set and at most polynomial growth in dimension N >= 3. We do this in terms of a bijection onto a set of polynomials describing the asymptotics of the solution. Furthermore we prove that coincidence sets of global solutions that are compact are also convex if the solution has at most quadratic growth. (C) 2021 Elsevier Ltd. All rights reserved.
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