Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
On the nodal set of the second eigenfunction of the laplacian in symmetric domains in
We present a simple proof of the fact that if is a bounded domain in , , which is convex and symmetric with respect to orthogonal directions, , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues must intersect the boundary. This result was proved by Payne in the case for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.
Monotonicity and symmetry of solutions of -Laplace equations, , via the moving plane method
Some nonexistence results for positive solutions of elliptic equations in unbounded domains.
Monotonicity and symmetry of solutions of -Laplace equations, , via the moving plane method
We present some monotonicity and symmetry results for positive solutions of the equation satisfying an homogeneous Dirichlet boundary condition in a bounded domain . We assume 1 < p < 2 and locally Lipschitz continuous and we do not require any hypothesis on the critical set of the solution. In particular we get that if is a ball then the solutions are radially symmetric and strictly radially decreasing.
A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle
Liouville results for -Laplace equations of Lane-Emden-Fowler type
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