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.
Cite this article
Antoine Henrot, Andrew Acker, Mikayel Poghosyan, Henrik Shahgholian, The multi-layer free boundary problem for the p-Laplacian in convex domains. Interfaces Free Bound. 6 (2004), no. 1, pp. 81–103DOI 10.4171/IFB/92