Calculus of Variations and Geometric Measure Theory

G. Ciraolo - R. Corso - A. Roncoroni

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

created by roncoroni on 05 Nov 2020


Accepted Paper

Inserted: 5 nov 2020
Last Updated: 5 nov 2020

Journal: Journal of Functional Analysis
Year: 2020

ArXiv: 2003.11759 PDF


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.