Bandle, C.; Brillard, A. Nonlinear elliptic equations involving critical Sobolev exponents: Asymptotic analysis via methods of epi-convergence. (English) Zbl 0808.35031 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. Cited in 2 Documents 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 PDF BibTeX XML Cite \textit{C. Bandle} and \textit{A. Brillard}, Z. Anal. Anwend. 13, No. 4, 615--628 (1994; Zbl 0808.35031) Full Text: DOI OpenURL