60 citations · 125 across the 25 of their papers we have counts for
26 papers
A geometric approach to nonlocal 2-Hessian equations
Fernando Charro, María del Mar González, María Soria-Carro
We study a nonlocal 2-Hessian equation, given by an infimum of linear deformations of the fractional Laplacian, that is, . We characterize…
Traveling-wave behavior for Fisher-KPP equations in the hyperbolic space
María del Mar González, Irene Gonzálvez, Fernando Quirós
We study the Cauchy problem in the hyperbolic space for the heat equation with a Fisher-KPP type forcing term. Depending on the relative strength of diffusion, measured by the infi…
A gluing construction of singular solutions for a fully non-linear equation in conformal geometry
María Fernanda Espinal, María del Mar González
In this paper we study the --Yamabe equation, , for solutions with a prescribed singular set given by a disjoint union of closed submanifolds whose dimension is posit…
Multiplicity of singular solutions to the fractional Yamabe problem on spheres
Renato G. Bettiol, María del Mar González, Ali Maalaoui
We prove nonuniqueness results for complete metrics with constant positive fractional curvature conformal to the round metric on , using bifurcation techniques.…
Concentration limit for non-local dissipative convection-diffusion kernels on the hyperbolic space
María del Mar González, Liviu I. Ignat, Dragoş Manea +1
We study a non-local evolution equation on the hyperbolic space . We first consider a model for particle transport governed by a non-local interaction kernel defined…
A Steklov version of the Torsional Rigidity
Lorenzo Brasco, María del Mar González, Mikel Ispizua
Motivated by the connection between the first eigenvalue of the Dirichlet-Laplacian and the torsional rigidity, the aim of this paper is to find a physically coherent and mathemati…
Deterministic Decoupling of Global Features and its Application to Data Analysis
Eduardo Martinez-Enriquez, Maria del Mar Gonzalez, Javier Portilla
We introduce a method for deterministic decoupling of global features and show its applicability to improve data analysis performance, as well as to open new venues for feature tra…
Bulk-Boundary eigenvalues for Bilaplacian problems
Davide Buoso, Carles Falcó, María del Mar González +1
We initiate the study of a bulk-boundary eigenvalue problem for the Bilaplacian with a particular third order boundary condition that arises from the study of dynamical boundary co…
Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality
Weiwei Ao, Azahara DelaTorre, Maria del Mar Gonzalez
In this paper, we will consider the fractional Caffarelli-Kohn-Nirenberg inequality \begin{equation*} Λ \left(\int_{\mathbb R^n}\frac{|u(x)|^{p}}{|x|^{β {p}}}\,dx\right)^{\frac{2}{…
-convergence of variational functionals with boundary terms in Stein manifolds
Eleonora Cinti, Bruno Franchi, María del Mar González
Let be an open subset of a Stein manifold and let be its boundary. It is well known that inherits a natural contact structure. In this paper we consider a family of…
Fractional Laplacians and extension problems: the higher rank case
Maria del Mar Gonzalez, Mariel Saez
The aim of this paper is two-fold: first, we look at the fractional Laplacian and the conformal fractional Laplacian from the general framework of representation theory on symmetri…
Recent progress on the fractional Laplacian in conformal geometry
Maria del Mar Gonzalez
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE…
A gluing approach for the fractional Yamabe problem with isolated singularities
Weiwei Ao, Azahara DelaTorre, Maria del Mar Gonzalez +1
We construct solutions for the fractional Yamabe problem that are singular at a prescribed number of isolated points. This seems to be the first time that a gluing method is succes…
Fractional powers of the wave operator via Dirichlet-to-Neumann maps in anti-de Sitter spaces
Alberto Enciso, María del Mar González, Bruno Vergara
We show that the fractional wave operator, which is usually studied in the context of hypersingular integrals but had not yet appeared in mathematical physics, can be constructed a…
A nonlocal diffusion problem on manifolds
Catherine Bandle, Maria del Mar Gonzalez, Marco A. Fontelos +1
In this paper we study a nonlocal diffusion problem on a manifold. These kind of equations can model diffusions when there are long range effects and have been widely studied in Eu…
Delaunay-type singular solutions for the fractional Yamabe Problem
A. DelaTorre, M. del Pino, M. d. M. Gonzalez +1
We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity $(-Δ)^γw = c_{n, γ} w^{\frac{n+2γ}{n-2γ}}, w>0 \ \mbox{in} \ \mathbb{R}^n \backs…
Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations
Yi Fang, Maria del Mar Gonzalez
In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We…
An extension problem for the CR fractional Laplacian
Rupert L. Frank, María de Mar González, Dario D. Monticelli +1
We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the…
Instability and bifurcation in a trend depending price formation model
María del Mar González, Maria Pia Gualdani, Joan Solà-Morales
A well-known model due to J.-M. Lasry and P.L. Lions that presents the evolution of prices in a market as the evolution of a free boundary in a diffusion equation is suggested to b…
Some constructions for the fractional Laplacian on noncompact manifolds
Valeria Banica, Maria del Mar González, Mariel Sáez
We give a definition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by Caffarelli-Silvestre. While this definition in the compact…
A discrete Bernoulli free boundary problem
Maria del Mar Gonzalez, Maria Gualdani, Henrik Shahgholian
We consider a free boundary problem for the -Laplace operator which is related to the so-called Bernoulli free boundary problem. In this formulation, the classical boundary grad…
Fractional conformal Laplacians and fractional Yamabe problems
Maria del Mar Gonzalez, Jie Qing
Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems…
Slow motion of particle systems as a limit of a reaction-diffusion equation with half-Laplacian in dimension one
Maria del Mar Gonzalez, Regis Monneau
We consider a reaction-diffusion equation with a half-Laplacian. In the case where the solution is independent on time, the model reduces to the Peierls-Nabarro model describing di…
Fractional Laplacian in Conformal Geometry
Sun-Yung Alice Chang, Maria del Mar Gonzalez
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli-Silvestre and a class of conformally covariant operat…