11 citations · 34 across the 9 of their papers we have counts for
10 papers
A Bernstein problem for translating solutions to the mean curvature flow
Juan Davila, Manuel del Pino, Juncheng Wei
We study entire graphical translating solutions of the mean curvature flow, \[ \operatorname{div}\!\left(\frac{\nabla G}{\sqrt{1+|\nabla G|^2}}\right) =\frac{1}{\sqrt{1+|\nabla G|^…
Interacting helical traveling waves for the Gross-Pitaevskii equation
Juan Dávila, Manuel del Pino, María Medina +1
We consider the 3D Gross-Pitaevskii equation \begin{equation}\nonumber i\partial_t ψ+Δψ+(1-|ψ|^2)ψ=0 \text{ for } ψ:\mathbb{R}\times \mathbb{R}^3 \rightarrow \mathbb{C} \end{equati…
Travelling helices and the vortex filament conjecture in the incompressible Euler equations
Juan Dávila, Manuel del Pino, Monica Musso +1
We consider the Euler equations in expressed in vorticity form. A classical question that goes back to Helmholtz is to describe the evolution of solutions with a hi…
Long-time asymptotics for evolutionary crystal dislocation models
Matteo Cozzi, Juan Dávila, Manuel del Pino
We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equation…
Nonlocal Delaunay surfaces
Juan Dávila, Manuel del Pino, Serena Dipierro +1
We construct codimension 1 surfaces of any dimension that minimize a periodic nonlocal perimeter functional among surfaces that are periodic, cylindrically symmetric and decreasing…
Bubbling solutions for nonlocal elliptic problems
Juan Dávila, Luis López Ríos, Yannick Sire
We investigate bubbling solutions for the nonlocal equation \[ A_Ω^s u =u^p,\ u >0 \quad \mbox{in } Ω, \] under homogeneous Dirichlet conditions, where is a bounded and smooth…
Nonlocal -minimal surfaces and Lawson cones
Juan Dávila, Manuel del Pino, Juncheng Wei
The nonlocal -fractional minimal surface equation for where is an open set in is given by $$ H_Σ^ s (p) := \int_{R^N} \frac {χ_E(x) - χ_{E^c}(x)} {|x-p…
Concentrating standing waves for the fractional nonlinear Schrödinger equation
Juan Dávila, Manuel del Pino, Juncheng Wei
We consider the semilinear equation where , is a sufficiently smo…
Regular solutions to a supercritical elliptic problem in exterior domains
Juan Dávila, Luis F. López
We consider the supercritical elliptic problem -Δu = λe^u, λ> 0, in an exterior domain under zero Dirichlet condition, where D is smooth and bounded i…
Regularity of radial extremal solutions for some non local semilinear equations
Antonio Capella, Juan Dávila, Louis Dupaigne +1
We investigate stable solutions of elliptic equations of the type \begin{equation*} \left \{ \begin{aligned} (-Δ)^s u&=λf(u) \qquad {\mbox{ in }} \\ u&= 0 \qqua…