The moving plane method for singular semilinear elliptic problems
Annamaria Canino, Luigi Montoro, Berardino Sciunzi
TL;DR
This paper develops a refined moving plane method to establish symmetry and monotonicity of positive solutions to singular semilinear elliptic problems with zero boundary conditions.
Contribution
It introduces a novel refinement of the moving plane technique applicable to singular nonlinearities in elliptic PDEs, broadening the scope of symmetry results.
Findings
Proves symmetry of solutions under general conditions
Establishes monotonicity properties of solutions
Applicable to a wide class of singular nonlinearities
Abstract
We consider positive solutions to semilinear elliptic problems with singular nonlinearities, under zero Dirichlet boundary condition. We exploit a refined version of the moving plane method to prove symmetry and monotonicity properties of the solutions, under general assumptions on the nonlinearity.
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