Non-convexity of level sets in convex rings for semilinear elliptic problems
نویسنده
چکیده
We show that there is a convex ring R = Ω \Ω ⊂ R in which there exists a solution u to a semilinear partial differential equation ∆u = f(u), u = −1 on ∂Ω, u = 1 on ∂Ω, with level sets, not all convex. Moreover every bounded solution u has at least one nonconvex level set. In our construction, the nonlinearity f , is non-positive, and smooth. AMS Classification: 35J60, 35R35.
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