We consider positive weak solutions to (Formula presented.) in (Formula presented.) under zero Dirichlet boundary condition. The domain (Formula presented.) is bounded or is the whole space, and the solution has a singularity on the singular set (Formula presented.). Under suitable assumptions on f we prove symmetry and monotonicity properties of the solutions when the singular set (Formula presented.) has zero s-capacity.
Qualitative properties of singular solutions to nonlocal problems
Punzo, Fabio;
2018-01-01
Abstract
We consider positive weak solutions to (Formula presented.) in (Formula presented.) under zero Dirichlet boundary condition. The domain (Formula presented.) is bounded or is the whole space, and the solution has a singularity on the singular set (Formula presented.). Under suitable assumptions on f we prove symmetry and monotonicity properties of the solutions when the singular set (Formula presented.) has zero s-capacity.File in questo prodotto:
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