The limit as in a two-phase free boundary problem for the -Laplacian

  • Julio D. Rossi

    Universidad de Buenos Aires, Argentina
  • Peiyong Wang

    Wayne State University, Detroit, USA

Abstract

In this paper, we study the limit as goes to infinity of a minimizer of a variational problem that is a two-phase free boundary problem of phase transition for the -Laplacian. Under a geometric compatibility condition, we prove that this limit is a solution of a free boundary problem for the -Laplacian. When the compatibility condition does not hold, we prove that there still exists a uniform limit that is a solution of a minimization problem for the Lipschitz constant. Moreover, we provide, in the latter case, an example that shows that the free boundary condition can be lost in the limit.

Cite this article

Julio D. Rossi, Peiyong Wang, The limit as in a two-phase free boundary problem for the -Laplacian. Interfaces Free Bound. 18 (2016), no. 1, pp. 115–135

DOI 10.4171/IFB/359