Best constants in some exponential Sobolev inequalities

• Autores: Bernd Kawohl, Marcello Lucia
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 57, Nº 4, 2008, págs. 1907-1928
• Idioma: inglés
• DOI: 10.1512/iumj.2008.57.3307
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• Resumen

  • A Pohozaev identity is used to classify the radial solutions of a quasilinear equation with exponential nonlinearity. The results are applied to find the infimum of the non-local functional F(?,u)=1n?O|?u|ndx-?F(?Oeudx),u?W01,n(O), for various nonlinearities F , where O is a bounded domain of Rn and ? a real parameter. Our results generalize the case when F(s)=logs.