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A Trudinger–Moser inequality in a weighted Sobolev space and applications
Author(s) -
Furtado Marcelo F.,
Medeiros Everaldo S.,
Severo Uberlandio B.
Publication year - 2014
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.201200315
Subject(s) - mathematics , sobolev space , space (punctuation) , inequality , sobolev inequality , exponential function , pure mathematics , type (biology) , mathematical analysis , dual (grammatical number) , function (biology) , art , ecology , philosophy , linguistics , literature , evolutionary biology , biology
We establish a Trudinger–Moser type inequality in a weighted Sobolev space. The inequality is applied in the study of the elliptic equation − div ( K ( x ) ∇ u ) = K ( x ) f ( u ) + hinR 2 , where K ( x ) = exp ( | x | 2 / 4 ) , f has exponential critical growth and h belongs to the dual of an appropriate function space. We prove that the problem has at least two weak solutions provided h ≠ 0 is small.