Let be a general, possibly non-smooth, bounded domain of , . Let be the critical Sobolev exponent. We study the following variational problem
investigating its asymptotic behavior as goes to zero, by means of -convergence techniques.We also show that sequences of maximizers concentrate energy at one point .
Cite this article
Giampiero Palatucci, Subcritical Approximation of the Sobolev Quotient and a Related Concentration Result. Rend. Sem. Mat. Univ. Padova 125 (2011), pp. 1–14DOI 10.4171/RSMUP/125-1