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EnglishWe 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.
| Titolo: | Quasilinear elliptic equations with critical potentials |
| Autori: | |
| Data di pubblicazione: | 2017 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11368/2901628 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1515/anona-2017-0091 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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http://hdl.handle.net/11368/2901628
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