We study Liouville theorems for problems of the form divL(A (x, u, ∇Lu)) + V(x)|u|p−2u = a(x)|u|q−1u on RN in the framework of Carnot groups. Here A is a vector-valued function satisfying Carathéodory condition and ∇L denotes an horizontal gradient, V is a given singular potential, a is a measurable scalar function and q > p − 1. Particular emphasis is given to the case when V is a Hardy or Gagliardo–Nirenberg potential. The results are new even in the canonical Euclidean setting.

Quasilinear elliptic equations with critical potentials

MITIDIERI, ENZO
2017

Abstract

We study Liouville theorems for problems of the form divL(A (x, u, ∇Lu)) + V(x)|u|p−2u = a(x)|u|q−1u on RN in the framework of Carnot groups. Here A is a vector-valued function satisfying Carathéodory condition and ∇L denotes an horizontal gradient, V is a given singular potential, a is a measurable scalar function and q > p − 1. Particular emphasis is given to the case when V is a Hardy or Gagliardo–Nirenberg potential. The results are new even in the canonical Euclidean setting.
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https://www.degruyter.com/document/doi/10.1515/anona-2017-0091/html
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2901628
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