Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary

  • Catherine Bandle

    Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
  • Moshe Marcus

    Department of Mathematics, Technion I.I.T., 32000 Haifa, Israel

Abstract

By means of comparison functions the asymptotic behaviour of solutions of semilinear elliptic equations which blow up at the boundary is established. The results depend only on the principal part of the second order operator and can be expressed in a simple way in terms of the associated Riemannian metric. In order to discuss the asymptotic behaviour of the derivatives a blowup technique together with a scaling argument is used.

Résumé

On utilise des fonctions de comparaison afin d’établir Ie comportement asymptotique des solutions de problèmes elliptiques semilinéaires qui explosent au bord. Les résultats s’expriment de manière simple à l’aide de Ia métrique de Riemann associée à cet opérateur. L’étude des dérivées repose sur une technique de blowup et utilise une invariance de groupe des solutions.

Cite this article

Catherine Bandle, Moshe Marcus, Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary. Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), no. 2, pp. 155–171

DOI 10.1016/S0294-1449(16)30162-7