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The free boundary of a semilinear elliptic equation. (English) Zbl 0561.35033
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
35J65 Nonlinear boundary value problems for linear elliptic equations
35R35 Free boundary problems for PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs