Monotonicity up to radially symmetric cores of positive solutions to nonlinear elliptic equations: local moving planes and unique continuation in a non-Lipschitz case

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Date
2004
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Sujet
Dead cores; Cores; Local symmetry; Unique continuation; Hopf's lemma; Maximum principle; Comparison techniques; Non-Lipschitz nonlinearities; Positivity; Symmetry; Monotonicity; Scalar field equations; Elliptic equations
Journal issue
Nonlinear Analysis: Theory, Methods & Applications
Volume
58
Number
3-4
Publication date
2004
Article pages
299-317
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.na.2004.04.007
URI
https://basepub.dauphine.fr/handle/123456789/6380
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Author
Felmer, Patricio
Dolbeault, Jean
Type
Article accepté pour publication ou publié
Abstract (EN)
We prove local monotonicity and symmetry properties for nonnegative solutions of scalar field equations with nonlinearities which are not Lipschitz. Our main tools are a local moving plane method and a unique continuation argument.