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Symmetry properties for positive solutions of elliptic equations with mixed boundary conditions

dc.contributor.authorBerestycki, Henri
dc.contributor.authorPacella, Filomena
dc.date.accessioned2014-05-20T14:48:40Z
dc.date.available2014-05-20T14:48:40Z
dc.date.issued1989
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13350
dc.language.isoenen
dc.subjectelliptic equationsen
dc.subject.ddc515en
dc.titleSymmetry properties for positive solutions of elliptic equations with mixed boundary conditionsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper we establish symmetry results for positive solutions of semilinear elliptic equations of the type Δu + f(u) = 0 with mixed boundary conditions in bounded domains. In particular we prove that any positive solution u of such an equation in a spherical sector ∑(α, R) is spherically symmetric if α, the amplitude of the sector, is such that 0 < α ⩽ π. By constructing counterexamples we show that this result is optimal in the sense that it does not hold for sectors bE(α, R) with amplitude π < α < 2π. More general symmetry properties are established for positive solutions in domains with axial symmetry. These results extend the well-known theorems of B. Gidas, W. M. Ni, and L. Nirenberg [Comm. Math. Phys.68 (1979), 209–243] to sector-like domains and mixed boundary conditions.en
dc.relation.isversionofjnlnameJournal of Functional Analysis
dc.relation.isversionofjnlvol87en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate1989
dc.relation.isversionofjnlpages177-211en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/0022-1236(89)90007-4en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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