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22 papers · 1 filter
An infinity Laplace equation with gradient term and mixed boundary conditions
Scott N. Armstrong, Charles K. Smart, Stephanie J. Somersille
We obtain existence, uniqueness, and stability results for the modified 1-homogeneous infinity Laplace equation \[ -Δ_\infty u - β|Du| = f, \] subject to Dirichlet or mixed Dirichl…
Almost everywhere well-posedness of continuity equations with measure initial data
Luigi Ambrosio, Alessio Figalli
The aim of this note is to present some new results concerning "almost everywhere" well-posedness and stability of continuity equations with measure initial data. The proofs of all…
Nonlocal minimal surfaces
L. A. Caffarelli, J. -M. Roquejoffre, O. Savin
The de Giorgi theory for minimal surfaces consists in studying sets whose indicator function is a (local) minimum of the BV norm. In this paper we replace the BV norm by the …
Some remarks on singular solutions of nonlinear elliptic equations. I
Luis Caffarelli, YanYan Li, Louis Nirenberg
The paper concerns singular solutions of nonlinear elliptic equations.
Global existence and uniqueness of solutions to a model of price formation
Lincoln Chayes, Maria del Mar Gonzalez, Maria Pia Gualdani +1
We study a model due to J.M. Lasry and P.L. Lions, describing the evolution of a scalar price which is realized as a free boundary in a 1-D diffusion equation with dynamically evol…
Global regularity of solutions to systems of reaction-diffusion with Sub-Quadratic Growth in any dimension
M. Cristina Caputo, Alexis Vasseur
This paper is devoted to the study of the regularity of solutions to some systems of reaction--diffusion equations, with reaction terms having a subquadratic growth. We show the gl…