Quasi-concavity for Semilinear Elliptic Equations with Non-monotone and Anisotropic Nonlinearities
نویسنده
چکیده
An interesting field of modern mathematical research is the study of geometric properties of solutions to elliptic problems. Remarkably, this is often done without any explicit representation of the solution. This paper concentrates on the problem of convexity of level sets for solutions to some elliptic semilinear boundary-value problems in convex rings.More precisely, letΩ0,Ω1 be convex, bounded domains in RN , N ≥ 2, satisfying 0∈Ω1 andΩ1 ⊂Ω0 (mnemonic: 0= outer, 1= inner). The domain Ω=Ω0 \Ω1 is said a convex ring. Consider the following problem:
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