5 papers · 1 filter
Survey on topological methods for Allen--Cahn equations and systems
João Henrique Andrade, Stefano Nardulli, Raonà Ponciano
We present a survey on multiplicity results for the Allen--Cahn equation and systems in the singular perturbation regime, emphasizing their geometric interpretation through -co…
Sharp Sobolev inequalities on noncompact Riemannian manifolds with bounded Ricci curvature
Carlo Morpurgo, Stefano Nardulli, Liuyu Qin
Given a smooth, complete Riemannian manifold with bounded Ricci curvature and positive injectivity radius, we derive a sharp Sobolev inequality for the embedding of $W^{1,p}(M)…
Multiplicity of solutions for Gross-Pitaevskii equations on Riemannian manifolds
Dario Corona, Stefano Nardulli, Ramon Oliver-Bonafoux +1
We provide a multiplicity result for solutions of time-independent Gross-Pitaevskii equations on closed Riemannian manifolds. Such solutions arise as (possibly non-minimizing) crit…
Interior regularity of area minimizing currents within a -submanifold
Stefano Nardulli, Reinaldo Resende
Given an area-minimizing integral -current in , we prove that the Hausdorff dimension of the interior singular set of cannot exceed , provided that is an embed…
From bubbles to clusters: Multiple solutions to the Allen--Cahn system
João Henrique de Andrade, Dario Corona, Stefano Nardulli +2
We extend previous works on the multiplicity of solutions to the Allen-Cahn system on closed Riemannian manifolds by considering an arbitrary number of phases. Specifically, we sho…