This paper deals with symmetry phenomena for solutions to the Dirichlet problem involving semilinear PDEs on Riemannian domains. We shall present a rather general framework where the symmetry problem can be formulated and provide some evidence that this framework is completely natural by pointing out some results for stable solutions. The case of manifolds with density, and corresponding weighted Laplacians, is inserted in the picture from the very beginning.
Bisterzo, A., Pigola, S. (2023). Symmetry of solutions to semilinear PDEs on Riemannian domains. NONLINEAR ANALYSIS, 234(September 2023) [10.1016/j.na.2023.113320].
Symmetry of solutions to semilinear PDEs on Riemannian domains
Bisterzo A.
;Pigola S.
2023
Abstract
This paper deals with symmetry phenomena for solutions to the Dirichlet problem involving semilinear PDEs on Riemannian domains. We shall present a rather general framework where the symmetry problem can be formulated and provide some evidence that this framework is completely natural by pointing out some results for stable solutions. The case of manifolds with density, and corresponding weighted Laplacians, is inserted in the picture from the very beginning.
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