Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions
Giulio Ciraolo, Rosario Corso, Alberto Roncoroni
Abstract
We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.
Topics & Concepts
MathematicsNeumann boundary conditionRobin boundary conditionBoundary (topology)Class (philosophy)Nonlinear systemTRACE (psycholinguistics)Regular polygonBoundary value problemMathematical analysisPure mathematicsGeometryLinguisticsPhysicsArtificial intelligenceComputer scienceQuantum mechanicsPhilosophyNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems