arXiv subjects

Azahara DelaTorre

Publications and source records attributed to Azahara DelaTorre.

20 records · Page 2Linked to original sources

arXiv2017

Improved Adams-type inequalities and their extremals in dimension 2m

In this paper we prove the existence of extremal functions for the Adams-Moser-Trudinger inequality on the Sobolev space $H^{m}(Ω)$, where $Ω$ is any bounded, smooth, open subset of $\mathbb{R}^{2m}$, $m\ge 1$. Moreover, we extend this result to improved versions of Adams' inequality of Adimurthi-Druet type. Our strategy is based on blow-up analysis for sequences of subcritical extremals and introduces several new techniques and constructions. The most important one is a new procedure for obtaining capacity-type estimates on annular regions.

math.AP↗

arXiv2015

Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry

We introduce the study of isolated singularities for a semilinear equation involving the fractional Laplacian. In conformal geometry, it is equivalent to the study of singular metrics with constant fractional curvature. Our main ideas are: first, to set the problem into a natural geometric framework, and second, to perform some kind of phase portrait study for this non-local ODE.

math.AP↗