Multiple Integrals of Lipschitz Functions in the Calculus of Variations.
Abstract
The author considers a multiple integral problem in the calculus of variations in which the integrand is locally Lipschitz but not differentiable, and in which minimization takes place over a Sobolev space. Using a minimax theorem, the author derives an analogue of the classical Euler condition for optimally, couched in terms of 'generalized gradients'. The author proceeds to indicate how these results may be applied to deduce existence and smoothness properties of solutions to certain Poisson equations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1976
- Accession Number
- ADA029963
Entities
People
- Frank H. Clarke
Organizations
- University of Wisconsin–Madison