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

Felmer, Patricio; Dolbeault, Jean (2004), Monotonicity up to radially symmetric cores of positive solutions to nonlinear elliptic equations: local moving planes and unique continuation in a non-Lipschitz case, Nonlinear Analysis: Theory, Methods & Applications, 58, 3-4, p. 299-317. http://dx.doi.org/10.1016/j.na.2004.04.007

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Type
Article accepté pour publication ou publié
Date
2004
Journal name
Nonlinear Analysis: Theory, Methods & Applications
Volume
58
Number
3-4
Publisher
Elsevier
Pages
299-317
Publication identifier
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Author(s)
Felmer, Patricio
Dolbeault, Jean cc
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.
Subjects / Keywords
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