26 citations · 61 across the 16 of their papers we have counts for
20 papers
Kazdan-Warner obstructions for a 4order boundary problem
Sergio Cruz-Blázquez, Azahara DelaTorre
We derive Kazdan-Warner type identities for the boundary problem of prescribing nonconstant interior curvature and boundary curvature on the upper hemisphere $\mathbb{S}^4_…
Classification of fractional, singular Yamabe metrics on a twice punctured sphere I
João Henrique Andrade, Azahara DelaTorre, João Marcos do Ò +2
The Delaunay metrics form a family of conformally flat, constant fractional Q-curvature metrics on a twice-punctured sphere. They are all (after a Möbius transformation) rotational…
A note on the first Steklov eigenvalue on planar domains
Azahara DelaTorre, Gabriele Mancini, Angela Pistoia +1
We consider the first positive Steklov eigenvalue on planar domains. First, we provide an example of a planar domain for which a first eigenfunction has a closed nodal line. Second…
On Hopf's Lemma for sign-changing supersolutions to fractional Laplacian equations
Azahara DelaTorre, Enea Parini
In this paper we investigate the validity of Hopf's Lemma for a (possibly sign-changing) function satisfying \[ (-Δ)^s u(x) \geq c(x)u(x) \quad \text{in }Ω,\] wher…
Conformal metrics on the four-dimensional half sphere with symmetric and curvatures
Sergio Cruz-Blázquez, Azahara DelaTorre
In this paper, we address the problem of prescribing non-constant and boundary curvatures on the upper hemisphere , via a conformal chan…
Non-degeneracy of the bubble in a fractional and singular 1D Liouville equation
Azahara DelaTorre, Gabriele Mancini, Angela Pistoia +1
We prove the non-degeneracy of solutions to a fractional and singular Liouville equation defined on the whole real line in presence of a singular term. We use conformal transformat…
Uniqueness of least energy solutions to the fractional Lane-Emden equation in the ball
Azahara DelaTorre, Enea Parini
We prove uniqueness of least-energy solutions to the fractional Lane-Emden equation, under homogeneous Dirichlet exterior conditions, when the underlying domain is a ball $B \subse…
Qualitative Properties of Singular Solutions to the Fractional Yamabe Problem
Sergio Cruz-Blázquez, Azahara DelaTorre, David Ruiz
In this paper we are interested in the qualitative properties of the solutions to the fractional Yamabe problem in which present an isolated singularity. In particul…
From fractional Lane-Emden-Serrin equation -- existence, multiplicity and local behaviors via classical ODE -- to fractional Yamabe metrics with singularity of "maximal" dimension
Hardy Chan, Azahara DelaTorre
Point singularities of solutions to the classical Lane-Emden-Serrin equation have a polyhomogeneous asymptotic expansion whose logarithmic corrections are determined by a first ord…
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}{…
Sign-changing solutions for the one-dimensional non-local sinh-Poisson equation
Azahara DelaTorre, Gabriele Mancini, Angela Pistoia
We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval , under Dirichlet conditions in the…
An analytic construction of singular solutions related to a critical Yamabe problem
Hardy Chan, Azahara DelaTorre
We answer affirmatively a question of Aviles posed in 1983, concerning the construction of singular solutions of semilinear equations without using phase-plane analysis. Fully expl…
ODE-methods in non-local equations
Weiwei Ao, Hardy Chan, Azahara DelaTorre +3
Non-local equations cannot be treated using classical ODE theorems. Nevertheless, several new methods have been introduced in the non-local gluing scheme of our previous article "O…
Concentration phenomena for the fractional -curvature equation in dimension 3 and fractional Poisson formulas
Azahara DelaTorre, Maria del Mar Gonzalez, Ali Hyder +1
We study the compactness properties of metrics of prescribed fractional -curvature of order in . We will use an approach inspired from conformal geometry, seeing a met…
The non-local mean-field equation on an interval
Azahara DelaTorre, Ali Hyder, Luca Martinazzi +1
We consider the fractional mean-field equation on the interval subject to Dirichlet boundary conditions, and prove…
On higher dimensional singularities for the fractional Yamabe problem: a non-local Mazzeo-Pacard program
Weiwei Ao, Hardy Chan, Azahara DelaTorre +3
We consider the problem of constructing solutions to the fractional Yamabe problem that are singular at a given smooth sub-manifold, and we establish the classical gluing method of…
Improved Adams-type inequalities and their extremals in dimension 2m
Azahara DelaTorre, Gabriele Mancini
In this paper we prove the existence of extremal functions for the Adams-Moser-Trudinger inequality on the Sobolev space , where is any bounded, smooth, open subset o…
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…
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…
Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry
Azahara DelaTorre, María del Mar González
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 metr…