6533b854fe1ef96bd12af4bd

RESEARCH PRODUCT

Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions

Giulio CiraoloRosario CorsoAlberto Roncoroni

subject

Class (set theory)Trace (linear algebra)010102 general mathematicsRegular polygon01 natural sciencesRobin boundary conditionNon-existenceNonlinear systemClassification of solutionsMathematics - Analysis of PDEsSettore MAT/05 - Analisi Matematica0103 physical sciencesQuasilinear anisotropic elliptic equationsFOS: MathematicsLiouville-type theoremApplied mathematics010307 mathematical physicsIntegral formula0101 mathematicsAnalysisMathematicsAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2021-01-01
10.1016/j.jfa.2020.108787http://hdl.handle.net/11311/1220905