JournalszaaVol. 13, No. 4pp. 615–628

Nonlinear Elliptic Equations Involving Critical Sobolev Exponents: Asymptotic Analysis via Methods of Epi-Convergence

  • Catherine Bandle

    Aesch/BL, Switzerland
  • A. Brillard

    Université de Haute Alsace, Mulhouse, France
Nonlinear Elliptic Equations Involving Critical Sobolev Exponents: Asymptotic Analysis via Methods of Epi-Convergence cover
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Abstract

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.

Cite this article

Catherine Bandle, A. Brillard, Nonlinear Elliptic Equations Involving Critical Sobolev Exponents: Asymptotic Analysis via Methods of Epi-Convergence. Z. Anal. Anwend. 13 (1994), no. 4, pp. 615–628

DOI 10.4171/ZAA/488