We consider a class of nonlocal conservation laws with exponential kernel and prove that
quantities involving the nonlocal term $ W:=\mathbb {1} _ {(-\infty, 0]}(\cdot)\exp …

Given any strictly convex norm‖·‖ on R 2 that is C 1 in R 2∖{0}, we study the generalized
Aviles-Giga functional I ϵ (m):=∫ Ω (ϵ|∇ m| 2+ 1 ϵ (1−‖ m‖ 2) 2) dx, for Ω⊂ R 2 and m …

This paper characterizes equivalence conditions on entire solutions to eikonal-type
nonlinear partial differential equations uz 1 2+ uz 2 2= p (z 1, z 2) eg (z 1, z 2) in C 2 with two …

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 the singularly perturbed problem F ε (u, Ω):=∫ Ω ε|∇ 2 u| 2+ ε-1| 1-|∇ u| 2| 2 on
bounded domains Ω⊂ R 2. Under appropriate boundary conditions, we prove that if Ω is an …

Motivated by some models of pattern formation involving an unoriented director field in the
plane, we study a family of unoriented counterparts to the Aviles–Giga functional. We …

We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-
connected bounded domain. Configurations of vanishing energy have been characterized …

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 …