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Best Sobolev constants and quasi‐linear elliptic equations with critical growth on spheres
Author(s) -
Bandle C.,
Peletier L. A.,
Stingelin S.
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410312
Subject(s) - mathematics , symmetrization , sobolev space , spheres , geodesic , type (biology) , compact space , mathematical analysis , elliptic curve , pure mathematics , physics , ecology , astronomy , biology
Sharp existence and nonexistence results for positive solutions of quasilinear elliptic equations with critical growth in geodesic balls on spheres are established. The arguments are based on Pohozaev type identities and asymptotic estimates for Emden–Fowler type equations. By means of spherical symmetrization and the concentration‐compactness principle existence and nonexistence results for general domains on spheres are obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)