66 citations · 99 across the 15 of their papers we have counts for
5 papers · 1 filter
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…
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*…
Equivalence of weak and viscosity solutions in fractional non-homogeneous problems
Begoña Barrios, Maria Medina
We establish the equivalence between the notions of weak and viscosity solutions for non-homogeneous equations whose main operator is the fractional p-Laplacian and the lower order…
Blow-up analysis of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures
Aleks Jevnikar, Rafael López-Soriano, María Medina +1
This paper is concerned with the compactness of metrics of the disk with prescribed Gaussian and geodesic curvatures. We consider a blowing-up sequence of metrics and give a precis…
Doubling nodal solutions to the Yamabe equation in with maximal rank
Maria Medina, Monica Musso
We construct a new family of entire solutions to the Yamabe equation $$-Δu=\frac{n(n-2)}{4}|u|^{\frac{4}{n-2}}u \mbox{ in }\mathcal{D}^{1,2}(\mathbb{R}^n).$$ If , our solution…