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 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
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
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
arXiv id
Title
link
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