The free boundary of a semilinear elliptic equation. (English) Zbl 0561.35033

Phillips, D.

Variational methods for equilibrium problems of fluids, Meet. Trento/Italy 1983, Astérisque 118, 205-210 (1984).

[For the entire collection see Zbl 0544.00035.]
In this paper, the author reports on a joint week with A. Friedman which concerns some semilinear elliptic equations, with a discontinuous nonlinearity. Estimates and geometrical properties of the level set corresponding to the discontinuity are given.

Reviewer: P.L.Lions

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
35R35	Free boundary problems for PDEs
35A30	Geometric theory, characteristics, transformations in context of PDEs

Keywords:

free boundary; convexity of level sets; semilinear elliptic equations; discontinuous nonlinearity; Estimates; geometrical properties

Citations:

Zbl 0544.00035