Phillips, D. 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 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 PDF BibTeX XML OpenURL