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2014 Comparison principle and constrained radial symmetry for the subdiffusive $p$-Laplacian
Antonio Greco
Publ. Mat. 58(2): 485-498 (2014).


A comparison principle for the subdiffusive $p$-Laplacian in a possibly non-smooth and unbounded open set is proved. The result requires that the involved sub and supersolution are positive, and the ratio of the former to the latter is bounded. As an application, constrained radial symmetry for overdetermined problems is obtained. More precisely, both Dirichlet and Neumann conditions are prescribed on the boundary of a bounded open set, and the Neumann condition depends on the distance from the origin. The domain of the problem, unknown at the beginning, turns out to be a ball centered at the origin if a positive solution exists. Counterexamples are also discussed.


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Antonio Greco. "Comparison principle and constrained radial symmetry for the subdiffusive $p$-Laplacian." Publ. Mat. 58 (2) 485 - 498, 2014.


Published: 2014
First available in Project Euclid: 21 July 2014

zbMATH: 1304.62035
MathSciNet: MR3264508

Primary: 35B06 , 35N25 , 35R35

Keywords: Comparison principle , overdetermined problems , radial symmetry , Subdiffusive $p$-Laplacian

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. 2 • 2014
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