English

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

Analysis of PDEs 2020-03-27 v1

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.

Keywords

Cite

@article{arxiv.2003.11759,
  title  = {Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions},
  author = {Giulio Ciraolo and Rosario Corso and Alberto Roncoroni},
  journal= {arXiv preprint arXiv:2003.11759},
  year   = {2020}
}