6 papers
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…