JournalsifbVol. 6 , No. 1DOI 10.4171/ifb/92

The multi-layer free boundary problem for the p-Laplacian in convex domains

  • Antoine Henrot

    Université de Lorraine, Vandoeuvre-les-Nancy, France
  • Andrew Acker

    Wichita State University, USA
  • Mikayel Poghosyan

    Yerevan State University, Armenia
  • Henrik Shahgholian

    KTH Royal Institute of Technology, Stockholm, Sweden
The multi-layer free boundary problem for the p-Laplacian in convex domains cover

Abstract

The main result of this paper concerns existence of classical solutions to the multi-layer Bernoulli free boundary problem with nonlinear joining conditions and the p-Laplacian as governing operator. The present treatment of the 2-layer case involves technical refinements of the one-layer case, studied earlier by two of the authors. The existence treatment of the multi-layer case is largely based on a reduction to the two-layer case, in which uniform separation of the free boundaries plays a key role.