88 citations · 134 across the 23 of their papers we have counts for
10 papers · 1 filter
Explicit minimisers for anisotropic Riesz energies
Rupert L. Frank, Joan Mateu, Maria Giovanna Mora +3
In this paper we describe explicitly the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisot…
Explicit minimisers for anisotropic Coulomb energies in 3D
Joan Mateu, Maria Giovanna Mora, Luca Rondi +2
In this paper we consider a general class of anisotropic energies in three dimensions and give a complete characterisation of their minimisers. We show that, depending on the Fouri…
Stability of ellipsoids as the energy minimisers of perturbed Coulomb energies
Joan Mateu, Maria Giovanna Mora, Luca Rondi +2
In this paper we characterise the minimiser for a class of nonlocal perturbations of the Coulomb energy. We show that the minimiser is the normalised characteristic function of an…
The global regularity of vortex patches revisited
Joan Verdera
We prove persistence of the regularity of the boundary of vortex patches for a large class of transport equations in the plane. The velocity field is given by convolution of the vo…
The regularity of the boundary of vortex patches for some non-linear transport equations
J. C. Cantero, J. Mateu, J. Orobitg +1
We prove the persistence of boundary smoothness of vortex patches for a non-linear transport equation in with velocity field given by convolution of the density with…
The equilibrium measure for an anisotropic nonlocal energy
J. A. Carrillo, J. Mateu, M. G. Mora +3
In this paper we characterise the minimisers of a one-parameter family of nonlocal and anisotropic energies defined on probability measures in , with . The ene…
The ellipse law: Kirchhoff meets dislocations
J. A. Carrillo, J. Mateu, M. G. Mora +3
In this paper we consider a nonlocal energy whose kernel is obtained by adding to the Coulomb potential an anisotropic term weighted by a parameter . The case …
The regularity of the boundary of a multidimensional aggregation patch
Andrea Bertozzi, John Garnett, Thomas Laurent +1
Let and let be the fundamental solution of the Laplace equation in We consider the aggregation equation $$ \frac{\partial ρ}{\partial t} + \operatorname{div…
Doubly connected V-states for the planar Euler equations
Taoufik Hmidi, Francisco de la Hoz, Joan Mateu +1
We prove existence of doubly connected V-states for the planar Euler equations which are not annuli. The proof proceeds by bifurcation from annuli at simple "eigenvalues". The bifu…
On rotating doubly connected vortices
Taoufik Hmidi, Joan Mateu, Joan Verdera
In this paper we consider rotating doubly connected vortex patches for the Euler equations in the plane. When the inner interface is an ellipse we show that the exterior interface…