Archive

Lecture Notes and Research Papers

Here you can find a list of the arXiv postings by participants to the RTG grant, and lecture notes on research topics in Analysis. Please note that lecture notes for the Introductory Lectures in Analysis and PDE are found in the Events page.

Lecture Notes

Lecture Notes on Elliptic and Parabolic PDE

Notes on linear semigroups and gradient flows, by Francesco Maggi

De Giorgi’s proof of the C^{0,alpha}-regularity theorem for elliptic equations with measurable coefficients, by Francesco Maggi

2021 arXiv postings

arXiv id

title

link

2106.03825

On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate, by Thomas Chen and Michael Hott

2104.14480

A Rigorous Derivation of a Boltzmann System for a Mixture of Hard-Sphere Gases, by Ioakeim Ampatzoglou, Joseph K. Miller, and Nataša Pavlović

2103.10946

From many-body quantum dynamics to the Hartree–Fock and Vlasov equations with singular potentials, by Jacky J. Chong, Laurent Lafleche, and Chiara Saffirio

2020 arXiv postings

arXiv id

title

link

2012.14779

Fractional elliptic equations in nondivergence form: definition, applications and Harnack inequality, by P. R. Stinga and M. Vaughan

2012.09261

Sharp a-contraction estimates for small extremal shocks, William Golding, Sam Krupa, Alexis Vasseur

2010.04761

Uniqueness and weak-BV stability for 2×2conservation laws, by Geng Chen, Sam G. Krupa and Alexis F. Vasseur

2009.14291

Second derivatives estimate of suitable solutions to the 3D Navier-Stokes equations, by Alexis Vasseur and Jincheng Yang

2009.12603

Instability for Axisymmetric Blow-up Solutions to Incompressible Euler Equations, by Laurent Lafleche, Alexis F. Vasseur, and Misha Vishik

2009.10352

Convergence and Error Estimates for the Conservative Spectral Method for Fokker-Planck-Landau Equations, by Clark A. Pennie and Irene M. Gamba

2008.05588

Construction of Maximal Functions associated with Skewed Cylinders Generated by Incompressible Flows and Applications, by Jincheng Yang

2008.04492

A One-Dimensional Variational Problem for Cholesteric Liquid Crystals with Disparate Elastic Constants, by Dmitry Golovaty, Michael Novack, and Peter Sternberg

2008.01753

Global estimates for the Hartree-Fock-Bogoliubov equations, by Jacky Jia Wei Chong, Manoussos G. Grillakis, Matei Machedon, and Zehua Zhao

2007.14868

Smoothness of collapsed regions in a capillarity model for soap films, by Darren King, Francesco Maggi, Salvatore Stuvard

2007.07962

Compactness and sharp lower bound for a 2D smectics model, by Michael Novack and Xiaodong Yan

2007.05654

Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics, by Luis Caffarelli and Ignacio Tomasetti

2007.03078

A direct approach to nonuniqueness and failure of compactness for the SQG equation, by Philip Isett and Andrew Ma

2007.00446

Rigorous derivation of a binary-ternary Boltzmann equation for a dense gas of hard spheres, by Ioakeim Ampatzoglou and Natasa Pavlovic

2006.15073

From the Peierls-Nabarro model to the equation of motion of the dislocation continuum, by Stefania Patrizi and Tharathep Sangsawang

2004.07322

Regularity for C1,α interface transmission problems, by L. A. Caffarelli, M. Soria-Carro, P. R. Stinga

2004.04140

Mean-Field Convergence of Point Vortices without Regularity, by Matthew Rosenzweig

2002.06273

Collapsing and the convex hull property in a soap film capillarity model, by Darren King, Francesco Maggi, Salvatore Stuvard

2001.09204

Propagation of Lpβ-norm, 1<p, for the system of Boltzmann equations for monatomic gas mixtures, by Erica de la Canal, Irene M. Gamba, Milana Pavić-Čolić

2019 arXiv postings

arXiv id

Title

link

1912.07585

The Mean-Field Limit of the Lieb-Liniger Model, by Matthew Rosenzweig

1911.12526

L^2-type contraction of viscous shocks for large family of scalar conservation laws, by Logan Stokols

1910.14476

Global well-posedness of a binary-ternary Boltzmann equation, by Ioakeim Ampatzoglou, Irene M. Gamba, Natasa Pavlovic, Maja Taskovic

1910.03110

Entropy Decay Rates for Conservative Spectral Schemes Modeling Fokker-Planck-Landau Type Flows in the Mean Field Limit, by Clark A. Pennie, Irene M. Gamba

1910.06959

Poisson Commuting Energies for a System of Infinitely Many Bosons, by Dana Mendelson, Andrea R. Nahmod, Nataša Pavlović, Matthew Rosenzweig, Gigliola Staffilani

1908.03847

A Rigorous Derivation of the Hamiltonian Structure for the Nonlinear Schrödinger Equation, by  Dana Mendelson, Andrea R. Nahmod, Nataša Pavlović, Matthew Rosenzweig, Gigliola Staffilani

1907.02483

Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates, by Thomas Chen, Ryan Denlinger, Nataša Pavlović

1907.00551

Plateau’s problem as a singular limit of capillarity problems, by Darren King, Francesco Maggi, Salvatore Stuvard

1906.00251

Holder Regularity up to the Boundary for Critical SQG on Bounded Domains, by Logan Stokols, Alexis Vasseur

1904.09468

Stability and uniqueness for piecewise smooth solutions to Burgers-Hilbert among a large class of solutions, by Sam G. Krupa and Alexis F. Vasseur.

1903.04279

A rigorous derivation of a ternary Boltzmann equation for a classical system of particles, by Ioakeim Ampatzoglou, Natasa Pavlovic