Gladiali, Francesca Maria and Grossi, Massimo (2004) Strict convexity of level sets of solutions of some nonlinear elliptic equations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 134 (2), p. 363-373. eISSN 1473-7124. Article.
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In this paper we study the convexity of the level sets of solutions of the problem where f is a suitable function with subcritical or critical growth. Under some assumptions on the Gauss curvature of ∂Ω, we prove that the level sets of the solution of (0.1) are strictly convex.
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