Luis F. López | Searcharxiv

arXiv2013

Rigidity results for non local phase transitions in the Heisenberg group $H$

In the Heisenberg group framework, we study rigidity properties for stable solutions of $(-Δ_H)^s v = f(v)$ in $H$, $s \in (0,1)$. We obtain a Poincaré type inequality in connection with a degenerate elliptic equation in $\R^4_+$; through an extension (or "lifting") procedure, this inequality will be then used for giving a criterion under which the level sets of the above solutions are minimal surfaces in $H$, i.e. they have vanishing mean curvature.

math.AP↗

arXiv2013

Regular solutions to a supercritical elliptic problem in exterior domains

We consider the supercritical elliptic problem -Δu = λe^u, λ> 0, in an exterior domain $Ω= \mathbb{R}^N \setminus D$ under zero Dirichlet condition, where D is smooth and bounded in \mathbb{R}^N, N greater or equal than 3. We prove that, for λsmall, this problem admits infinitely many regular solutions.

math.AP↗