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.

Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions / G. Ciraolo, R. Corso, A. Roncoroni. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 280:1(2021 Jan 01). [10.1016/j.jfa.2020.108787]

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

G. Ciraolo
;
2021

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.
Classification of solutions; Liouville-type theorem; Non-existence; Quasilinear anisotropic elliptic equations
Settore MAT/05 - Analisi Matematica
1-gen-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/798458
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