13 citations · 15 across the 7 of their papers we have counts for
4 papers · 1 filter
Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality
Guido De Philippis, Luca Gennaioli, Alessandro Pigati +1
We prove mass estimates for PDE-constrained measures on sets of -finite -measure, assuming an appropriate rank condition. As an application, we derive a Michael-…
Michael-Simon inequality for anisotropic energies close to the area via multilinear Kakeya-type bounds
Guido De Philippis, Alessandro Pigati
Given an anisotropic integrand , we can generalize the classical isotropic area by looking at the functional $$\mathcal{F}(Σ^k):=\int_ΣF(T…
Decay of excess for the abelian Higgs model
Guido De Philippis, Aria Halavati, Alessandro Pigati
In this article we prove that entire critical points of the self-dual -Yang-Mills-Higgs functional , with energy $$E_1(u,\nabla;B_R):=\int_{B_R}\left[|\nabl…
Free boundary minimal surfaces: a nonlocal approach
Alessandro Pigati, Francesca Da Lio
Given a -smooth closed embedded manifold , with , and a compact connected smooth Riemannian surface with $\partial S\neq\emptys…