Critical points of the Trudinger–Moser trace functional with high energy levels

  • Shengbing Deng

    Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
  • Monica Musso

    Departamento de Matemática, Pontificia Universidad Catolica de Chile, Avda. Vicuña Mackenna 4860, Macul, Chile

Abstract

Let be a bounded domain in with smooth boundary. In this paper we are concerned with the existence of critical points for the supercritical Trudinger–Moser trace functional

in the set , where is an integer and is a small parameter. For any integer and for any sufficiently small, we prove the existence of a pair of -peaks constrained critical points of the above problem.

Cite this article

Shengbing Deng, Monica Musso, Critical points of the Trudinger–Moser trace functional with high energy levels. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 1, pp. 59–95

DOI 10.1016/J.ANIHPC.2013.10.002