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Liouville Theorems for Stable Weak Solutions of Elliptic Problems Involving Grushin Operator

Authors: 

Phuong Le

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

23.png

where Ω is a bounded or unbounded C1 domain of 24.png 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 4_LePhuong.png and f. We also show the sharpness of our results when Ω = 14.png and f has power or exponential growth.