Gradient maximum principle for minima

Authors:
C. Mariconda;G. Treu
Affiliations:
Associate Professor, Faculty of Engineering, University of Padova, Padova, Italy;Associate Professor, Facuity of Statistical Sciences, University of Padova, Padova, Italy
Venue:
Journal of Optimization Theory and Applications
Year:
2002

Citing 3
Cited 0

Weakly differentiable functions

Weakly differentiable functions
Convex analysis and variational problems

Convex analysis and variational problems
On the Bounded Slope Condition and the Validity of the Euler Lagrange Equation

SIAM Journal on Control and Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We state a maximum principle for the gradient of the minima of integral functionals I(u) = ∫Ω[f(∇u)+g(u)]dx, on u+ W01,1(Ω), just assuming that I is strictly convex. We do not require that f, g be smooth, nor that they satisfy growth conditions. As an application, we prove a Lipschitz regularity result for constrained minima.