Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory
Rights accessRestricted access - confidentiality agreement
For nonnegative even kernels K, we consider the K-nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated K-nonlocal mean curvature equation in an open set O¿Rn, we built a calibration for the nonlocal perimeter inside O¿Rn. The calibrating functional is a nonlocal null-Lagrangian. As a consequence, we conclude the minimality in O of each leaf of the foliation. As an application, we prove the minimality of K-nonlocal minimal graphs and that they are the unique minimizers subject to their own exterior data. As a second application of the calibration, we give a simple proof of an important result from the seminal paper of Caffarelli, Roquejoffre, and Savin, stating that minimizers of the fractional perimeter are viscosity solutions.
The final publication is available at link.springer.com
CitationCabre, X. Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory. "Annali di matematica pura ed applicata", 4 Febrer 2020, vol. 199, p. 1979-1995.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder