Liouville Theorems for Stable Weak Solutions of Elliptic Problems Involving Grushin Operator
Liouville Theorems for Stable Weak Solutions of Elliptic Problems Involving Grushin Operator
Source title:
Communications on Pure and Applied Analysis, 19(1): 511-525,
2020
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
We consider the boundary value problem
where Ω is a bounded or unbounded C1 domain of are nonnegative functions, f is an increasing function, ∇G and divG are Grushin gradient and Grushin divergence, respectively. We prove some Liouville theorems for stable weak solutions of the problem under suitable assumptions on
and f. We also show the sharpness of our results when Ω =
and f has power or exponential growth.