We look at complete, locally conformally flat metrics defined on a domain Ω ⊂ S. There is a lot of information about the singular set ∂Ω contained in the positivity of σk and, in particular, we… (More)

Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems observed in [11],… (More)

We prove a Γ-convergence result for an energy functional related to some fractional powers of the Laplacian operator, (−∆) for 1/2 < s < 1, with two singular perturbations, that leads to a two-phase… (More)

In 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… (More)

We study the existence and asymptotics for large time of the solutions to a one dimensional evolution equation with non-standard right hand side. The right hand side involves the derivative of the… (More)

We 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 González and Qing. These are… (More)

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 community. The… (More)

We consider some nonstandard Sobolev spaces in one dimension, in which functions have different regularity in different subsets. These spaces are useful in the study of some nonlinear parabolic… (More)

We give a notion of renormalized weighted volume in the setting of conformal geometry following the ideas of Fefferman-Graham. Indeed, it is a precise term in the asymptotic expansion near the… (More)

We study a model due to J.M. Lasry and P.L. Lions describing the evolution of a scalar price which is realized as a free boundary in a 1D diffusion equation with dynamically evolving, non–standard… (More)