9 papers · 1 filter
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…
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…