A Trudinger–Moser inequality in a weighted Sobolev space and applications | Zendy

Furtado Marcelo F. | Zendy; Medeiros Everaldo S. | Zendy; Severo Uberlandio B. | Zendy

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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.

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