We study Liouville theorems for problems of the form divL (A (x, u, ∇L u)) + V(x)|u|p−2 u = a(x)|u|q−1 u 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
D'AMBROSIO, Lorenzo;
2017-01-01
Abstract
We study Liouville theorems for problems of the form divL (A (x, u, ∇L u)) + V(x)|u|p−2 u = a(x)|u|q−1 u 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.File in questo prodotto:
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