Geodesic
The limit as $p \to \infty$ in a two-phase free boundary problem for the $p$-Laplacian
Julio D. Rossi1 ; Peiyong Wang2
1Universidad de Buenos Aires, Argentina
2Wayne State University, Detroit, USA
Interfaces and free boundaries, Tome 18 (2016) no. 1, pp. 115-135

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DOI

In this paper, we study the limit as p goes to infinity of a minimizer of a variational problem that is a two-phase free boundary problem of phase transition for the p-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.
DOI : 10.4171/ifb/359
Classification : 35-XX, 49-XX
Mots-clés : Two-phase free boundary problem, phase transition, variational principle, p-Laplacian, infinity Laplacian

Julio D. Rossi  1   ; Peiyong Wang  2

1 Universidad de Buenos Aires, Argentina
2 Wayne State University, Detroit, USA 
Julio D. Rossi; Peiyong Wang. The limit as $p \to \infty$ in a two-phase free boundary problem for the $p$-Laplacian. Interfaces and free boundaries, Tome 18 (2016) no. 1, pp. 115-135. doi: 10.4171/ifb/359
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     title = {The limit as $p \to \infty$ in a two-phase free boundary problem for the $p${-Laplacian}},
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