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
2303.02281
Global Existence for the Landau Equation with small initial data, William Golding, Maria Gualdani, Amélie Loher
2303.05236
Layer separation of the 3D incompressible Navier-Stokes equation in a bounded domain, Alexis F. Vasseur and Jincheng Yang
arXiv id
title
link
2211.02758
Derivation of a Boltzmann equation with higher-order collisions from a generalized Kac model, Esteban Cárdenas, Nataša Pavlović, and William Warner
2211.15099
Interaction of a free boundary with a diffusion on a plane: analogy with the obstacle problem, Luis A. Caffarelli, Jean-Michel Roquejoffre, and Ignacio Tomasetti
2210.16376
A Heintze–Karcher inequality with free boundaries and applications to capillarity theory, Matias G. Delgadino and Daniel Weser
2210.09600
Moment estimates and well-posedness of the binary-ternary Boltzmann equation, Ioakeim Ampatzoglou, Irene M. Gamba, Nataša Pavlović, and Maja Tasković
2209.04532
Derivation of the 1-D Groma-Balogh equations from the Peierls-Nabarro model, Stefania Patrizi and Tharathep Sangsawang
2208.07911
On the semiclassical regularity of thermal equilibria, Jacky J. Chong, Laurent Lafleche, and Chiara Saffirio
2207.10209
Mean field games with common noise and degenerate idiosyncratic noise, Pierre Cardaliaguet, Benjamin Seeger, Panagiotis Souganidis
2207.07820
On an L2 critical Boltzmann equation, by Thomas Chen, Ryan Denlinger and Natasa Pavlovic
2206.12386
Rigidity theorems for best Sobolev inequalities, Francesco Maggi, Robin Neumayer, and Ignacio Tomasetti
2205.02951
Isoperimetric residues and a mesoscale flatness criterion for hypersurfaces with bounded mean curvature, Francesco Maggi and Michael Novack
2205.01872
A smectic liquid crystal model in the periodic setting, Michael Novack and Xiaodong Yan
2202.11583
Uniform stability in the Euclidean isoperimetric problem for the Allen–Cahn energy, Francesco Maggi and Daniel Restrepo
2202.13998
Global-in-time Semiclassical Regularity for the Hartree-Fock Equation, Jacky J. Chong, Laurent Lafleche, and Chiara Saffirio
arXiv id
title
link
2112.12119
On the Well-posedness and Stability of Cubic and Quintic Nonlinear Schrödinger Systems on T3, by Thomas Chen and Amie Urban
2111.1278
On a family of fully nonlinear integro-differential operators: From fractional Laplacian to nonlocal Monge-Ampère, Luis A. Caffarelli, María Soria-Carro
2110.02426
Boundary Vorticity Estimates for Navier-Stokes and Application to the Inviscid Limit, Alexis F. Vasseur and Jincheng Yang
2110.10337
The Neumann problem for fully nonlinear SPDE, Paul Gassiat and Benjamin Seeger
2109.03770
The norm of linear extension operators for Cm−1,1(Rn), Jacob Carruth, Abraham Frei-Pearson, and Arie Israel
2108.04390
Least Wasserstein distance between disjoint shapes with perimeter regularization, Michael Novack, Ihsan Topaloglu, and Raghavendra Venkatraman
2107.10463
Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential, William Golding, Maria Pia Gualdani, Nicola Zamponi
2106.05195
Nonlinear approximation of 3D smectic liquid crystals: sharp lower bound and compactness, Michael Novack and Xiaodong Yan
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