48 citations · 114 across the 21 of their papers we have counts for
23 papers
Asymptotically homogeneous solutions of the supercritical Lane-Emden system
Louis Dupaigne, Hatem Hajlaoui, Marius Ghergu
We consider the Lane-Emden system-u = |v| p-1 v,-v = |u| q-1 u in R d. When p q 1, it is known that there exists a positive radial stable solution (u, v) C…
Liouville-type theorems for the Lane-Emden equation in the half-space and cones
Louis Dupaigne, Alberto Farina, Troy Petitt
We prove that 0 the only classical solution of the Lane-Emden equation in the half-space which is stable outside a compact set. We also consider weak solutions and the case of gene…
Regularity and Symmetry for Semilinear Elliptic Equations in Bounded Domains
Louis Dupaigne, Alberto Farina
In the present paper, we investigate the regularity and symmetry properties of weak solutions to semilinear elliptic equations which are locally stable.
Sobolev's inequality under a curvature-dimension condition
Louis Dupaigne, Ivan Gentil, Simon Zugmeyer
In this note we present a new proof of Sobolev's inequality under a uniform lower bound of the Ricci curvature. This result was initially obtained in 1983 by Ilias. Our goal is to…
A Liouville-type theorem for the Lane-Emden equation in a half-space
Louis Dupaigne, Boyan Sirakov, Philippe Souplet
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem d…
Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains
Louis Dupaigne, ALberto Farina
We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.