Subcritical Approximation of the Sobolev Quotient and a Related Concentration Result

  • Giampiero Palatucci

    Università degli Studi di Parma, Italy

Abstract

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. 1–14

DOI 10.4171/RSMUP/125-1