14.2k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Istituto Nazionale di Fisica Nucleare, Sezione di PisaIT5.2k papers
- Centre National de la Recherche ScientifiqueFR3.2k papers
- Sapienza University of RomeIT3.1k papers
- Istituto Nazionale di Fisica Nucleare, Sezione di Roma IIT3k papers
- Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di FrascatiIT2.8k papers
- Institut National de Physique Nucléaire et de Physique des ParticulesFR2.7k papers
- The Ohio State UniversityUS2.7k papers
- University of BolognaIT2.7k papers
- Rutherford Appleton LaboratoryGB2.7k papers
- Istituto Nazionale di Fisica Nucleare, Sezione di GenovaIT2.6k papers
- University of Wisconsin–MadisonUS2.6k papers
- University of GenoaIT2.5k papers
13 papers · 2 filters
Low regularity solutions to the logarithmic Schrodinger equation
Rémi Carles, Masayuki Hayashi, Tohru Ozawa
We consider the logarithmic Schr{ö}dinger equation, in various geometric settings. We show that the flow map can be uniquely extended from H^1 to L^2 , and that this extension is L…
Lattice tilings minimizing nonlocal perimeters
Annalisa Cesaroni, Ilaria Fragalà, Matteo Novaga
We prove the existence of periodic tessellations of minimizing a general nonlocal perimeter functional, defined as the interaction between a set and its complement t…
The Cauchy problem for the logarithmic Schrödinger equation revisited
Masayuki Hayashi, Tohru Ozawa
We revisit the Cauchy problem for the logarithmic Schrödinger equation and construct strong solutions in , the energy space, and the -energy space. The solutions are prov…
Struwe's Global Compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini, Letizia Temperini
We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorg…
On the existence of minimizing sets for a weakly-repulsive non-local energy
Davide Carazzato, Aldo Pratelli, Ihsan Topaloglu
We consider a non-local interaction energy over bounded densities of fixed mass . We prove that under certain regularity assumptions on the interaction kernel these energies adm…
Reduced energies for thin ferromagnetic films with perpendicular anisotropy
G. Di Fratta, C. B. Muratov, V. V. Slastikov
We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring…
A short proof of Allard's and Brakke's regularity theorems
Guido De Philippis, Carlo Gasparetto, Felix Schulze
We give new short proofs of Allard's regularity theorem for varifolds with bounded first variation and Brakke's regularity theorem for integral Brakke flows with bounded forcing. T…
Thomas-Fermi theory of out-of-plane charge screening in graphene
Vitaly Moroz, Cyrill B. Muratov
This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas-Fermi theory. We est…
A variational model of charged drops in dielectrically matched binary fluids: the effect of charge discreteness
Cyrill B. Muratov, Matteo Novaga, Philip Zaleski
This paper addresses the ill-posedness of the classical Rayleigh variational model of conducting charged liquid drops by incorporating the discreteness of the elementary charges. I…
-gradient flow of convex functionals
Antonin Chambolle, Matteo Novaga
We are interested in the gradient flow of a general first order convex functional with respect to the -topology. By means of an implicit minimization scheme, we show existence…
Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem
Giulia Bevilacqua, Chiara Lonati
We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting…
Boundedness estimates for nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations
Francesca Anceschi, Mirco Piccinini
We investigate local regularity properties of weak solutions to a broad class of nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations. In particular, we focus on proving a…
Higher order boundary Harnack principle via degenerate equations
Susanna Terracini, Giorgio Tortone, Stefano Vita
As a first result we prove higher order Schauder estimates for solutions to singular/degenerate elliptic equations of type: \[ -\mathrm{div}\left(ρ^aA\nabla w\right)=ρ^af+\mathrm{d…