18 citations · 24 across the 5 of their papers we have counts for
6 papers · 1 filter
Caffarelli's work on elliptic free boundary problems
Camillo De Lellis
The aim of the note is to illustrate some of the ideas introduced by Luis Caffarelli in his groundbreaking works on the regularity theory for elliptic free boundary problems, in a…
A remark on the uniqueness of solutions to hyperbolic conservation laws
Alberto Bressan, Camillo De Lellis
Given a strictly hyperbolic system of conservation laws, it is well known that there exists a unique Lipschitz semigroup of weak solutions, defined on a domain of funct…
High dimensionality and h-principle in PDE
Camillo De Lellis, László Székelyhidi
In this note we would like to present "an analysts' point of view" on the Nash-Kuiper theorem and in particular highlight the very close connection to some aspects of turbulence --…
A regularizing property of the -eikonal equation
Camillo De Lellis, Radu Ignat
We prove that any -dimensional solution of the eikonal equation has locally Lipschitz gradient except at a locally finite number of vo…
Dissipative Euler flows with Onsager-critical spatial regularity
Tristan Buckmaster, Camillo De Lellis, László Székelyhidi
For any we show the existence of continuous periodic weak solutions of the Euler equations which do not conserve the kinetic energy and belong to the space $L^1_t (C_x^{\…
Dissipative continuous Euler flows in two and three dimensions
Antoine Choffrut, Camillo De Lellis, László Székelyhidi
Recently, two of these authors construct dissipative continuous (weak) solutions to the incompressible Euler equations on the three-dimensional torus . The building bl…