The Singular Set of Minima of Integral Functionals
Abstract
In this paper we provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals [inline-graphic not available: see fulltext] where F is suitably convex with respect to Dv and Hölder continuous with respect to (x,v). In particular, we prove that the Hausdorff dimension of the singular set is always strictly less than n, where [inline-graphic not available: see fulltext].
- Publication:
-
Archive for Rational Mechanics and Analysis
- Pub Date:
- June 2006
- DOI:
- 10.1007/s00205-005-0402-5
- Bibcode:
- 2006ArRMA.180..331K
- Keywords:
-
- Neural Network;
- Complex System;
- Nonlinear Dynamics;
- Electromagnetism;
- Integral Functional