Browsing by Author "González Nogueras, María del Mar"

A discrete bernoulli free boundary problem
González Nogueras, María del Mar; Gualdani, Maria; Shagholian, Henrick (201204)
External research report
Open AccessWe consider a free boundary problem for the pLaplace operator which is related to the socalled Bernoulli free boundary problem. In this formulation, the classical boundary gradient condition is replaced by a condition ... 
An extension problem for the CR fractional Laplacian
Frank, Rupert L.; González Nogueras, María del Mar; Monticelli, Dario D.; Tan, Jinggang (201312)
External research report
Open AccessWe show that the conformally invariant fractional powers of the subLaplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this ... 
An extension problem for the CR fractional Laplacian
Frank, Rupert L.; González Nogueras, María del Mar; Monticelli, Dario D.; Tan, Jinggang (20150101)
Article
Open AccessWe show that the conformally invariant fractional powers of the subLaplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this ... 
A perturbation argument for a MongeAmpere type equation arising in optimal transportation
González Nogueras, María del Mar; Caffarelli, Luis; Nguyen, Truyen (201111)
External research report
Open AccessWe prove some asymptotic interior regularity results for potential functions of optimal transportation problems with power costs. We show that our problems are equivalent to optimal transportation problems whose cost ... 
A Perturbation argument for a Monge–Ampère type equation arising in optimal transportation
Caffarelli, Luis; González Nogueras, María del Mar; Nguyen, Truyen (20140501)
Article
Restricted access  publisher's policyWe prove some interior regularity results for potential functions of optimal transportation problems with power costs. The main point is that our problem is equivalent to a new optimal transportation problem whose cost ... 
Asymptotic behavior of PalaisSmale sequences associated with fractional Yamabe type equations
González Nogueras, María del Mar; Fang, Yi (2014)
External research report
Open AccessIn this paper, we analyze the asymptotic behavior of PalaisSmale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that PalaisSmale sequences ... 
Asymptotic behavior of palaissmale sequences associated with fractional yamabetype equations
Fang, Yi; González Nogueras, María del Mar (20151201)
Article
Open AccessIn this paper, we analyze the asymptotic behavior of PalaisSmale sequences associated to fractional Yamabetype equations on an asymptotically hyperbolic Riemannian manifold. We prove that PalaisSmale sequences can be ... 
Classical solutions for a nonlinear FokkerPlanck equation arising in computational neuroscience
Carrillo, José A.; González Nogueras, María del Mar; Gualdani, Maria; Schonbek, Maria E. (201108)
External research report
Open AccessIn this paper we analyze the global existence of classical solutions to the initial boundaryvalue problem for a nonlinear parabolic equation describing the collective behavior of an ensemble of neurons. These equations ... 
Fracional Laplacian in conformal geometry
González Nogueras, María del Mar; Chang, SunYung Alice (201004)
Article
Restricted access  author's decisionIn this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Ca arelliSilvestre and a class of conformally covariantoperators in conformal geometry. 
Fracional Laplacian in conformal geometry
González Nogueras, María del Mar; Chang, SunYung Alice (201003)
External research report
Open AccessIn this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Ca arelliSilvestre and a class of conformally covariant operators in conformal geometry. 
Fractional conformal Laplacians and fractional Yamabe problems
González Nogueras, María del Mar; Qing, Jie (201012)
External research report
Open AccessBased on the relations between scattering operators of asymptotically hyperbolic metrics and DirichlettoNeumann operators of uniformly degenerate elliptic boundary value problems observed in [11], we formulate fractional ... 
Fractional Laplacian in conformal geometry
González Nogueras, María del Mar; Chang, SunYung Alice (20110130)
Article
Restricted access  publisher's policyIn this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal geometry. 
Fractional laplacian in conformal geometry
González Nogueras, María del Mar (20091207)
Lecture
Open Access 
Further results on the fractional Yamabe problem: the umbilic case
González Nogueras, María del Mar (2014)
External research report
Open AccessWe prove some existence results for the fractional Yamabe problem in the case that the boundary manifold is umbilic, thus covering some of the cases not considered by Gonz alez and Qing. These are inspired ... 
Gamma convergence of an energy functional related to the fractional Laplacian
González Nogueras, María del Mar (2009)
Article
Restricted access  publisher's policyWe prove a Γ convergence result for an energy functional related to some fractional powers of the Laplacian operator, (−Δ)s for 1/2 < s < 1, with two singular perturbations, that leads to a twophase problem. The case ... 
Instability and bifurcation in a trend depending price formation model
González Nogueras, María del Mar; Gualdani, Maria Pia; SolàMorales Rubió, Joan de (201608)
Article
Open AccessA wellknown 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 modified in order to show instabilities for some values ... 
Layer solutions for the fractional Laplacian on hyperbolic space
González Nogueras, María del Mar (2013)
Conference report
Open AccessThe workshop dealt with partial differential equations in ge om etry and technical applications. The main topics were the co mbination of nonlinear partial differential equations and geometric pro blems, and fourth order ... 
Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
González Nogueras, María del Mar; Saéz, Mariel; Sire, Yannick (20141201)
Article
Restricted access  publisher's policyWe investigate the equation; (Delta(Hn))(gamma) w = f(w) in Hn,; where (Delta(Hn))(gamma) corresponds to the fractional Laplacian on hyperbolic space for gamma is an element of(0, 1) and f is a smooth nonlinearity that ... 
Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
González Nogueras, María del Mar; Saéz, Mariel; Sire, Yannick (201212)
External research report
Open Accesswhere (¿ Hn) corresponds to the fractional Laplacian on hyperbolic space for 2 (0; 1) and f is a smooth nonlinearity that typically comes from a double well potential. We prove the existence of heteroclinic connections ... 
Renormalized weighted volume for the conformal fractional Laplacian
González Nogueras, María del Mar (201107)
External research report
Open AccessWe give a notion of renormalized weighted volume in the setting of conformal geometry following the ideas of FeffermanGraham. Indeed, it is a precise term in the asymptotic expansion near the boundary for a weighted ...