88 citations · 134 across the 23 of their papers we have counts for
31 papers
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…
Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension
J. Cufí, J. J. Donaire, P. Mattila +1
Consider a standard Cantor set in the plane of Hausdorff dimension 1. If the linear density of the associated measure vanishes, then the set of points where the principal value…
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…
Birth and life of the boundedness of the Cauchy Integral on Lipschitz graphs
Joan Verdera
We review various motives for considering the problem of estimating the Cauchy Singular Integral on Lipschitz graphs in the norm. We follow the thread that led to the solut…