A boundary-value problem for a semilinear elliptic equation in a convex ring is considered. Under suitable structural conditions, any classical solution u lying between its (constant) boundary values is shown to decrease along each ray starting from the origin, and to have convex level surfaces.
Quasi-concavity for semilinear elliptic equations with non-monotone and anisotropic nonlinearities
GRECO, ANTONIO
2006-01-01
Abstract
A boundary-value problem for a semilinear elliptic equation in a convex ring is considered. Under suitable structural conditions, any classical solution u lying between its (constant) boundary values is shown to decrease along each ray starting from the origin, and to have convex level surfaces.
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