Nonlinear elliptic equations involving critical Sobolev exponents: Asymptotic analysis via methods of epi-convergence. (English) Zbl 0808.35031

Bandle, C.; Brillard, A.

Z. Anal. Anwend. 13, No. 4, 615-628 (1994).

Summary: We study the minimizers of two functionals involving critical Sobolev exponents, and whose Euler equations lead to nonlinear boundary value problems. We first employ classical methods to obtain estimates. We then rephrase the problems in a more abstract functional analytical setting. We use epi-convergence arguments in order to describe the behaviour of the minimizers.

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
49J45	Methods involving semicontinuity and convergence; relaxation
35J20	Variational methods for second-order elliptic equations

Keywords:

minimizing sequence; critical Sobolev exponents; epi-convergence arguments