On Stable Solutions to a Weighted Degenerate Elliptic Equation with Advection Terms

In this paper, we study the elliptic equations where , is the Grushin operator. Here, the advection term is a smooth, divergence free vector field satisfying certain decay condition and is a continuous function such that , , where is the Grushin norm of . We will prove that the equation has no stabl...

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Bibliographic Details
Published in:Mathematical Notes 2022-08, Vol.112 (1-2), p.109-115
Main Authors: Quyet, Dao Trong, Thang, Dao Manh
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Advection
Continuity (mathematics)
Divergence
Elliptic functions
Fields (mathematics)
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:In this paper, we study the elliptic equations where , is the Grushin operator. Here, the advection term is a smooth, divergence free vector field satisfying certain decay condition and is a continuous function such that , , where is the Grushin norm of . We will prove that the equation has no stable solutions provided that where is the homogeneous dimension of associated to the Grushin operator.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434622070124