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

Rosario Corso, Giulio Ciraolo, Alberto Roncoroni

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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.
Original languageEnglish
Pages (from-to)1-27
Number of pages27
JournalJournal of Functional Analysis
Volume280
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • Analysis

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