38 citations · 135 across the 21 of their papers we have counts for
25 papers
Multi-peak solutions for a critical Choquard problem in dimension 2
Luca Battaglia, Wenshan Luo
We consider a Choquard problem in a smooth bounded domain in the plane. We show the existence of solutions which concentrate at a finite number of points. Up to our knowledge, this…
Prescribing nearly constant curvatures on balls
Luca Battaglia, Sergio Cruz-Blázquez, Angela Pistoia
In this paper we address two boundary cases of the classical Kazdan-Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvat…
On the shape of solutions to elliptic equations in possibly non convex planar domains
Luca Battaglia, Fabio De Regibus, Massimo Grossi
In this note we prove uniqueness of the critical point for positive solutions of elliptic problems in bounded planar domains: we first examine the Poisson problem - Delta u = f(x,y…
Non-uniqueness for the nonlocal Liouville equation in and applications
Luca Battaglia, Matteo Cozzi, Antonio J. Fernández +1
We construct multiple solutions to the nonlocal Liouville equation \begin{equation} \label{eqk} \tag{L} (-Δ)^{\frac{1}{2}} u = K(x) e^u \quad \mbox{ in } \mathbb{R}. \end{equation}…
A blow-up phenomenon for a non-local Liouville-type equation
Luca Battaglia, Maria Medina, Angela Pistoia
We consider a non-local Liouville equation corresponding to the prescription of the geodesic curvature on the circle. We build a family of solutions which blow up at a critical poi…
Prescribing Gaussian curvature on surfaces with conical singularities and geodesic boundary
Luca Battaglia, Aleks Jevnikar, Zhi-An Wang +1
We study conformal metrics with prescribed Gaussian curvature on surfaces with conical singularities and geodesic boundary in supercritical regimes. Exploiting a variational argume…
Large conformal metrics with prescribed Gaussian and geodesic curvatures
Luca Battaglia, Maria Medina, Angela Pistoia
We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on the unit disk. This is equivalent to solving the following P.D.E. \begin{equation*…
Asymptotic behavior of minimal solutions of as
Luca Battaglia, Francesca Gladiali, Massimo Grossi
We consider the Dirichlet problem with and non-negative and non-decreasing. We show existence and uniqueness of solutions for any and discuss their…
A double mean field equation related to a curvature prescription problem
Luca Battaglia, Rafael López-Soriano
We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger in…
Non-uniqueness of blowing-up solutions to the Gelfand problem
Luca Battaglia, Massimo Grossi, Angela Pistoia
We consider the Gelfand problem on a planar domain. Under some conditions on the potential, we provide the first examples of multiplicity for blowing-up solutions at a given point…
Uniform bounds for solutions to elliptic problems on simply connected planar domains
Luca Battaglia
We consider the singular Liouville equation and the Henon-Lane-Emden problem on simply connected planar domains. We show that any solution to each problem must satisfy a uniform bo…
A general existence result for stationary solutions to the Keller-Segel system
Luca Battaglia
We consider a Liouville-type PDE on a smooth bounded planar domain, which is related to stationary solutions of the Keller-Segel's model for chemotaxis. We prove existence of solut…
Groundstates of the Choquard equations with a sign-changing self-interaction potential
Luca Battaglia, Jean Van Schaftingen
We consider a nonlinear Choquard equation when the self-interaction potential is unbounded from below. Under…
Nonradial entire solutions for Liouville systems
Luca Battaglia, Francesca Gladiali, Massimo Grossi
We consider the following system of Liouville equations: $$\left\{\begin{array}{ll}-Δu_1=2e^{u_1}+μe^{u_2}&\text{in }\mathbb R^2\\-Δu_2=μe^{u_1}+2e^{u_2}&\text{in }\mathbb R^2\\\in…
Ground state solutions for a nonlinear Choquard equation
Luca Battaglia
We discuss the existence of ground state solutions for the Choquard equation We prove the existence of solutions under…
A unified approach of blow-up phenomena for two-dimensional singular Liouville systems
Luca Battaglia, Angela Pistoia
We consider generic 2 x 2 singular Liouville systems on a smooth bounded domain in the plane having some symmetry with respect to the origin. We construct a family of solutions to…
Existence of groundstates for a class of nonlinear Choquard equations in the plane
Luca Battaglia, Jean Van Schaftingen
We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation where is the…
B2 and G2 Toda systems on compact surfaces: a variational approach
Luca Battaglia
We consider the B2 and G2 Toda systems on compact surfaces. We attack the problem using variational techniques. We get existence and multiplicity of solutions under a topological a…
Existence and non-existence results for the SU(3) singular Toda system on compact surfaces
Luca Battaglia, Andrea Malchiodi
We consider the SU(3) Toda system on a compact surface. We give both existence and non-existence results under some conditions on the parameters. Existence results are obtained usi…
Moser-Trudinger inequalities for singular Liouville systems
Luca Battaglia
In this paper we prove a Moser-Trudinger inequality for the Euler-Lagrange functional of a general singular Liouville system. We characterize the values of the parameters which yie…
A note on compactness properties of the singular Toda system
Luca Battaglia, Gabriele Mancini
In this note, we consider blow-up for solutions of the SU(3) Toda system on a compact surface Σ. In particular, we give a complete proof of the compactness result stated by Jost, L…
Existence and multiplicity result for the singular Toda system
Luca Battaglia
We consider the Toda system on a compact surface. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when…
A Moser-Trudinger inequality for the singular Toda system
Luca Battaglia, Andrea Malchiodi
In this paper we prove a sharp version of the Moser-Trudinger inequality for the Euler-Lagrange functional of a singular Toda system, motivated by the study of models in Chern-Simo…
Remarks on the Moser-Trudinger inequality
Luca Battaglia, Gabriele Mancini
We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré's inequality. We find out that the same equivalence does not hold in general for conformal metr…