On the Evans-Krylov theorem (2009)
Caffarelli, Luis, Silvestre, Luis
In this note, motivated by our work on integral fully nonlinear equations, we provide a variation of the proof of Evans-Krylov theorem about the interior $C^{2,\alpha}$ a priori estimate for concave...
The Evans-Krylov theorem for non local fully non linear equations (2009)
Caffarelli, Luis, Silvestre, Luis
We prove an interior regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood in the classical sense. If we let...
Some remarks on singular solutions of nonlinear elliptic equations. I (2009)
Caffarelli, Luis, Li, YanYan, Nirenberg, Louis
The paper concerns singular solutions of nonlinear elliptic equations.
Regularity results for nonlocal equations by approximation (2009)
Caffarelli, Luis, Silvestre, Luis
In this paper we prove a nonlocal version of the Cordes-Niremberg estimates. We use it to extend our previous regularity results for fully nonlinear integro-differential equations to the variable...
Ambrosio, Luigi, Caffarelli, Luis, Crandall, Michael G., Evans, Lawrence C., Fusco, Nicola, Dacorogna, Bernard, ...
Regularity theory for fully nonlinear integro-differential equations (2007)
Caffarelli, Luis, Silvestre, Luis
We consider nonlinear integro-differential equations, like the ones that arise from stochastic control problems with purely jump L\`evy processes. We obtain a nonlocal version of the ABP estimate,...
Caffarelli, Luis, Salsa, Sandro, Silvestre, Luis
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent...
Sparse Random Graphs Methods, Structure, and Heuristics Publication No. (2007)
Daniel Turrin Fernholz, Vijaya Ramachandran Supervisor, Luis Caffarelli, Adam Klivans, Greg Plaxton, David Zuckerman, ...
This dissertation is an algorithmic study of sparse random graphs which are parametrized by the distribution of vertex degrees. Our contributions include: a formula for the diameter of various sparse...
An extension problem related to the fractional Laplacian (2006)
Caffarelli, Luis, Silvestre, Luis
The operator square root of the Laplacian $(-\lap)^{1/2}$ can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the...
Some multi-valued solutions to Monge-Ampere equations (2005)
We construct several types of multi-valued solutions to the Monge-Ampere equation in higher dimensions.
Stochastic Distributed Algorithms for Target Surveillance (2003)
Luis Caffarelli, Valentino Crespi, George Cybenko, Irene Gamba, Daniela Rus
this paper we investigate problems of target surveillance with the aim of building a general framework for the evaluation of the performance of a system of autonomous agents. To this purpose we...
On Maxwellian Equilibria of Insulated Semiconductors (2000)
Luis Caffarelli, Jean Dolbeault, Peter A. Markowich, Christian Schmeiser
. A semilinear elliptic integro-differential equation subject to homogeneous Neumann boundary conditions for the equilibrium potential in an insulated semiconductor device is considered. A...
On Maxwellian Equilibria of Insulated Semiconductors (2000)
Luis Caffarelli, Jean Dolbeault, Peter A. Markowich, Christian Schmeiser
A semilinear elliptic integro-differential equation subject to homogeneous Neumann boundary conditions for the equilibrium potential in an insulated semiconductor device is considered. A variational...