66 citations · 99 across the 15 of their papers we have counts for
19 papers
Higher-order asymptotic expansions and finite difference schemes for the fractional -Laplacian
Félix del Teso, María Medina, Pablo Ochoa
We propose a new asymptotic expansion for the fractional -Laplacian with precise computations of the errors. Our approximation is shown to hold in the whole range $p\in(1,\infty…
Segregated solutions for a critical elliptic system with a small interspecies repulsive force
Haixia Chen, Maria Medina, Angela Pistoia
We consider the elliptic system when and $β:=β_{i(q+1…
Equivalence of solutions for non-homogeneous p(x)-Laplace equations
María Medina, Pablo Ochoa
We establish the equivalence between weak and viscosity solutions for non-homogeneous -Laplace equations with a right-hand side term depending on the spatial variable, the un…
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…
A blow-up phenomenon for a non-local Liouville-type equation
Luca Battaglia, Maria Medina, Angela Pistoia
We consider a non-local Liouville equation corresponding to the prescription of the geodesic curvature on the circle. We build a family of solutions which blow up at a critical poi…
Large conformal metrics with prescribed Gaussian and geodesic curvatures
Luca Battaglia, Maria Medina, Angela Pistoia
We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on the unit disk. This is equivalent to solving the following P.D.E. \begin{equation*…
Equivalence of weak and viscosity solutions in fractional non-homogeneous problems
Begoña Barrios, Maria Medina
We establish the equivalence between the notions of weak and viscosity solutions for non-homogeneous equations whose main operator is the fractional p-Laplacian and the lower order…
Blow-up analysis of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures
Aleks Jevnikar, Rafael López-Soriano, María Medina +1
This paper is concerned with the compactness of metrics of the disk with prescribed Gaussian and geodesic curvatures. We consider a blowing-up sequence of metrics and give a precis…
Doubling nodal solutions to the Yamabe equation in with maximal rank
Maria Medina, Monica Musso
We construct a new family of entire solutions to the Yamabe equation $$-Δu=\frac{n(n-2)}{4}|u|^{\frac{4}{n-2}}u \mbox{ in }\mathcal{D}^{1,2}(\mathbb{R}^n).$$ If , our solution…
Interacting helical vortex filaments in the 3-dimensional Ginzburg-Landau equation
Juan Dávila, Manuel del Pino, Maria Medina +1
For each given , we construct a family of entire solutions , , with helical symmetry to the 3-dimensional complex-valued Ginzburg-Landa…
Desingularization of Clifford Torus and Nonradial Solutions to Yamabe Problem with Maximal Rank
María Medina, Monica Musso, Juncheng Wei
Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts-Kenig-Merle nodal nonradial solutions to the critical…
Principal Eigenvalue of Mixed Problem for the Fractional Laplacian: Moving the Boundary Conditions
Tommaso Leonori, Maria Medina, Ireneo Peral +2
We analyze the behavior of the eigenvalues of the following non local mixed problem $\left\{ \begin{array}{rcll} (-Δ)^{s} u &=& λ_1(D) \ u &\innΩ,\\ u&=&0&\inn D,\\ \mathcal{N}_{s}…
On viscosity and weak solutions for non-homogeneous p-Laplace equations
Maria Medina, Pablo Ochoa
In this manuscript we study the relation between viscosity and weak solutions for non-homogeneous p-Laplace equations with lower order term depending on , and . Mo…
A fractional elliptic problem in with critical growth and convex nonlinearities
Claudia Bucur, Maria Medina
In this paper we prove the existence of a positive solution of the nonlinear and nonlocal elliptic equation in \[ (-Δ)^s u =\varepsilon h u^q+u^{2_s^*-1} \] in the c…
Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions
Begoña Barrios, María Medina
We present some comparison results for solutions to certain non local elliptic and parabolic problems that involve the fractional Laplacian operator and mixed boundary conditions,…
The effect of the Hardy potential in some Calderón-Zygmund properties for the fractional Laplacian
Boumediene Abdellaoui, María Medina, Ireneo Peral +1
The goal of this paper is to study the effect of the Hardy potential on the existence and summability of solutions to a class of nonlocal elliptic problems $$ \left\{\begin{array}{…
Fractional elliptic problems with critical growth in the whole of
Serena Dipierro, Maria Medina, Enrico Valdinoci
We study the following nonlinear and nonlocal elliptic equation in~ $$ (-Δ)^s u = ε\,h\,u^q + u^p \ {\mbox{ in }}\R^n, $$ where~, , is a small paramete…
Optimal results for the fractional heat equation involving the Hardy potential
Boumediene Abdellaoui, María Medina, Ireneo Peral +1
In this paper we study the influence of the Hardy potential in the fractional heat equation. In particular, we consider the problem $$(P_θ)\quad \left\{ \begin{array}{rcl} u_t+(-Δ)…
Bifurcation results for a fractional elliptic equation with critical exponent in R^n
Serena Dipierro, Maria Medina, Ireneo Peral +1
In this paper we study some nonlinear elliptic equations in obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is $$ (-Δ)^s u = ε\…