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 …

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 …

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 …

We study the fine properties of a class of weak solutions u of the eikonal equation arising as
asymptotic domain of a family of energy functionals introduced in [T. Rivière and S. Serfaty …

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 …

Continuing the program initiated in Golovaty et al.(SIAM J Math Anal 51 (1): 276–320, 2018),
we analyze a model problem based on highly disparate elastic constants that we propose in …

We carry out an asymptotic analysis of a variational problem relevant in the studies of
nematic liquid crystalline films when one elastic constant dominates over the others, namely …

We prove the existence of generalized characteristics for weak, not necessarily entropic,
solutions of Burgers' equation∂ t u+∂ xu 2 2= 0, whose entropy productions are signed …

We consider entropy solutions to the eikonal equation in two-space dimensions. These
solutions are motivated by a class of variational problems and fail in general to have …

We prove the upper-tail Large Deviation Principle (LDP) for the parabolic Airy process and
characterize the limit shape of the directed landscape under the upper-tail conditioning. The …