63 citations · 476 across the 94 of their papers we have counts for
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A note on the regularity and the existence of Riemannian splines
Dario Corona, Roberto Giambò, Paolo Piccione
In this paper, we present a comprehensive proof concerning the regularity of critical points for the spline energy functional on Riemannian manifolds, even for the general higher-o…
Multiplicity results for mass constrained Allen-Cahn equations on Riemannian manifolds with boundary
Dario Corona, Stefano Nardulli, Ramon Oliver-Bonafoux +2
We present multiplicity results for mass constrained Allen-Cahn equations on a Riemannian manifold with boundary, considering both Neumann and Dirichlet conditions. These results h…
Quantitative stability of a nonlocal Sobolev inequality
Paolo Piccione, Minbo Yang, Shuneng Zhao
In this paper, we study the quantitative stability of the nonlocal Soblev inequality \begin{equation*} S_{HL}\left(\int_{\mathbb{R}^N}\big(|x|^{-μ} \ast |u|^{2_μ^{\ast}}\big)|u|^{2…
Multiplicity of solutions to the multiphasic Allen-Cahn-Hilliard system with a small volume constraint on closed parallelizable manifolds
João Henrique Andrade, Jackeline Conrado, Stefano Nardulli +2
We prove the existence of multiple solutions to the Allen--Cahn--Hilliard (ACH) vectorial equation (with two equations) involving a triple-well (triphasic) potential with a small v…
Lusternik-Schnirelman and Morse theory for the Van der Waals-Cahn-Hilliard equation with volume constraint
Vieri Benci, Dario Corona, Stefano Nardulli +2
We give a multiplicity result for solutions of the Van der Waals-Cahn-Hilliard two-phase transition equation with volume constraints on a closed Riemannian manifold. Our proof empl…
Van der Waals--Allen--Cahn--Hilliard equation with a volume constraint
Vieri Benci, Stefano Nardulli, Paolo Piccione
We give multiplicity results for the solutions of a nonlinear elliptic equation, with an asymmetric double well potential of Van der Waals-Allen--Cahn--Hilliard type, satisfying a…