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

2020 arXiv postings


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

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

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

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

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

2019 arXiv postings


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

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

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

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

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

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

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

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

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

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

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