Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift

B Fehrman, B Gess - Inventiones mathematicae, 2023 - Springer
Large deviations of conservative interacting particle systems, such as the zero range
process, about their hydrodynamic limit and their respective rate functions lead to the …

Hydrodynamic large deviations of TASEP

J Quastel, LC Tsai - Communications on Pure and Applied …, 2021 - Wiley Online Library
We consider the large deviations from the hydrodynamic limit of the Totally Asymmetric
Simple Exclusion Process (TASEP). This problem was studied by Jensen and Varadhan and …

Rigidity of a non-elliptic differential inclusion related to the Aviles–Giga conjecture

X Lamy, A Lorent, G Peng - Archive for Rational Mechanics and Analysis, 2020 - Springer
In this paper we prove sharp regularity for a differential inclusion into a set K ⊂ R^ 2 * 2 K⊂
R 2× 2 that arises in connection with the Aviles–Giga functional. The set K is not elliptic, and …

Optimal Besov differentiability for entropy solutions of the eikonal equation

F Ghiraldin, X Lamy - Communications on Pure and Applied …, 2020 - Wiley Online Library
Optimal Besov Differentiability for Entropy Solutions of the Eikonal Equation Page 1 Optimal
Besov Differentiability for Entropy Solutions of the Eikonal Equation FRANCESCO GHIRALDIN …

[HTML][HTML] The rectifiability of the entropy defect measure for Burgers equation

E Marconi - Journal of Functional Analysis, 2022 - Elsevier
We consider bounded weak solutions to the Burgers equation for which every entropy
dissipation is representable by a measure and we prove that all these measures are …

On the structure of weak solutions to scalar conservation laws with finite entropy production

E Marconi - Calculus of Variations and Partial Differential …, 2022 - Springer
We consider weak solutions with finite entropy production to the scalar conservation law ∂
_t u+ div _x F (u)= 0\quad in (0, T) * R^ d.∂ tu+ div x F (u)= 0 in (0, T)× R d. Building on the …

Factorization for entropy production of the Eikonal equation and regularity

A Lorent, G Peng - arXiv preprint arXiv:2104.01467, 2021 - arxiv.org
The Eikonal equation arises naturally in the limit of the second order Aviles-Giga functional
whose $\Gamma $-convergence is a long standing challenging problem. The theory of …

Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift

B Fehrman, B Gess - arXiv preprint arXiv:1910.11860, 2019 - arxiv.org
Large deviations of conservative interacting particle systems, such as the zero range
process, about their hydrodynamic limit and their respective rate functions lead to the …

On the concentration of entropy for scalar conservation laws

S Bianchini, E Marconi - DISCRETE AND CONTINUOUS DYNAMICAL …, 2016 - iris.sissa.it
We prove that the entropy for an $ L^\infty $-solution to a scalar conservation laws with
continuous initial data is concentrated on a countably $1 $-rectifiable set. To prove this result …

On the regularity of weak solutions to Burgers' equation with finite entropy production

X Lamy, F Otto - Calculus of Variations and Partial Differential …, 2018 - Springer
Bounded weak solutions of Burgers' equation ∂ _tu+ ∂ _x (u^ 2/2)= 0∂ tu+∂ x (u 2/2)= 0
that are not entropy solutions need in general not be BV. Nevertheless it is known that …