Symmetry Results for Solutions of Semilinear Elliptic Equations with Convex Nonlinearities

72 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Symmetry of solutions to semilinear elliptic equations via Morse index (2007, methodology): “More precisely, in [10] it was proved that if B is a ball or an annulus and f(|x|, s) is strictly convex in the s-variable, then any solution u to (1.”
Partial symmetry and asymptotic behavior for some elliptic variational problems (2003, background): “We also would like to point out an interesting recent work by Pacella [ 16 ] where the maximum principle is used to prove partial symmetry results for index 1 solutions of problems where moving plane fails.”
Symmetry of Solutions to Variational Problems for Nonlinear Elliptic Equations via Reflection Methods (2010, background): “(i) The special case j = 1, f convex had been considered earlier in [68, 71 ].”