4 papers · 1 filter
Carleman estimates for stationary -valued maps: a variational approach
Aria Halavati, Luca Spolaor
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizi…
New weighted inequalities on two-manifolds
Aria Halavati
We establish a new class of weighted Poincaré and elliptic functional inequalities on smooth two-manifolds with explicit constants, for a family of weights satisfying a diff…
Quantitative stability of Yang-Mills-Higgs instantons in two dimensions
Aria Halavati
We prove that if an N-vortex pair nearly minimizes the Yang-Mills-Higgs energy, then it is second order close to a minimizer. First we use new weighted inequalities in two dimensio…
Decay of excess for the abelian Higgs model
Guido De Philippis, Aria Halavati, Alessandro Pigati
In this article we prove that entire critical points of the self-dual -Yang-Mills-Higgs functional , with energy $$E_1(u,\nabla;B_R):=\int_{B_R}\left[|\nabl…