Liouville type theorems for elliptic equations involving Grushin operator and advection
Date
2017-04-25
Authors
Duong, Anh Tuan
Nguyen, Nhu Thang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the equation
-Gαu + ∇Gw ∙ ∇Gu = ∥x∥s|u|p-1u, x = (x, y) ∈ ℝN = ℝN1 x ℝN2,
where Gα (resp., ∇G) is Grushin operator (resp. Grushin gradient), p > 1 and s ≥ 0. The scalar function w satisfies a decay condition, and ∥x∥ is the norm corresponding to the Grushin distance. Based on the approach by Farina [8], we establish a Liouville type theorem for the class of stable sign-changing weak solutions. In particular, we show that the nonexistence result for stable positive classical solutions in [4] is still valid for the above equation.
Description
Keywords
Liouville type theorem, Stable weak solution, Grushin operator, Degenerate elliptic equation
Citation
Duong, A. T., & Nguyen, N. T. (2017). Liouville type theorems for elliptic equations involving Grushin operator and advection. <i>Electronic Journal of Differential Equations, 2017</i>(108), pp. 1-11.
Rights
Attribution 4.0 International