Monotonicity and symmetry of singular solutions to quasilinear problems
Francesco Esposito, Luigi Montoro, Berardino Sciunzi
TL;DR
This paper investigates the symmetry and monotonicity of singular solutions to quasilinear elliptic equations, using an improved moving plane method under certain nonlinearity conditions.
Contribution
It introduces an enhanced moving plane technique to establish symmetry and monotonicity of solutions with singularities in quasilinear elliptic problems.
Findings
Positive solutions exhibit symmetry and monotonicity.
The improved moving plane method effectively handles singular solutions.
Results depend on specific assumptions on the nonlinearity.
Abstract
We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved moving plane procedure.
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