An improvement for the Trudinger-Moser inequality and applications

作者：do O Jodo Marcos^*; de Souza Manasses; de Medeiros Everaldo; Severo Uberlandio

来源：Journal of Differential Equations, 2014, 256(4): 1317-1349.

DOI：10.1016/j.jde.2013.10.016

• Nonlinear elliptic equations
• Trudinger-Moser inequality
• Exponential critical growth
• Ground state solution

In line with the Concentration-Compactness Principle due to P.-L. Lions [19], we study the lack of compactness of Sobolev embedding of W-1,W-n (R-n), n >= 2, into the Orlicz space L-Phi alpha determined by the Young function Phi(alpha) (s) behaving like e(alpha vertical bar s vertical bar n/(n-1)) - 1 as vertical bar s vertical bar -> +infinity. In the light of this result we also study existence of ground state solutions for a class of quasilinear elliptic problems involving critical growth of the Trudinger-Moser type in the whole space R-n.

• 出版日期2014-2-15