Regular solutions to a supercritical elliptic problem in exterior domains

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

Regularity of radial extremal solutions for some non local semilinear equations

We investigate stable solutions of elliptic equations of the type \begin{equation*} \left \{ \begin{aligned} (-\Delta)^s u&=\lambda f(u) \qquad {\mbox{ in $B_1 \subset \R^{n}$}} \\ u&= 0 \qquad{\mbox{ on $\partial B_1$,}}\end{aligned}\right . \end{equation*} where $n\ge2$, $s \in (0,1)$, $\lambda \geq 0$ and $f$ is any smooth positive superlinear function. The operator $(-\Delta)^s$ stands for the fractional Laplacian, a pseudo-differential operator of order $2s$. According to the value of $\lambda$, we study the existence and regularity of weak solutions $u$

Nonlocal Delaunay surfaces

We construct codimension 1 surfaces of any dimension that minimize a periodic nonlocal perimeter functional among surfaces that are periodic, cylindrically symmetric and decreasing. These surfaces may be seen as a nonlocal analogue of the classical Delaunay surfaces (onduloids). For small volume, most of their mass tends to be concentrated in a periodic array and the surfaces are close to a periodic array of balls (in fact, we give explicit quantitative bounds on these facts)

La Operación Acordeón: Condiciones de validez según el tribunal constitucional peruano

El Tribunal Constitucional con el objeto de determinar la relevancia constitucional del derecho de suscripción preferente en las operaciones acordeón, advirtió que este tipo de operación societaria no se encontraba regulada en nuestro sistema jurídico, siendo necesario determinar su legitimidad constitucional a fin validar su ejecución en la práctica empresarial. Sin embargo, la advertencia del potencial riesgo que genera para los accionistas la operación acordeón, implicó la necesidad de determinar también cuáles deben ser las condiciones para considerar válida esta operación societaria. A continuación, analizaremos qué es una operación acordeón, su legitimidad constitucional, condiciones de validez y cuál es la importancia del derecho de suscripción preferente en este tipo de operación societaria

Nonlinear problems with solutions exhibiting a free boundary on the boundary

We prove existence of nonnegative solutions to -Delta u + u = 0 on a smooth bounded domain Omega subject to the singular boundary derivative condition partial derivative u/partial derivative v = -u(-beta) + lambda f (x, u) on partial derivative Omega boolean AND {u > 0} with 0 lambda* we show the existence of a maximal positive solution. We analyze its linearized stability and its regularity. Minimizers of the energy functional related to the problem are shown to be regular and satisfy the equation together with the boundary condition