Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Strict convexity, strong ellipticity, and regularity in the calculus of variations

J. M. Balla1*

a1 University of California, Berkeley

In this paper we investigate the connection between strong ellipticity and the regularity of weak solutions to the equations of nonlinear elastostatics and other nonlinear systems arising from the calculus of variations. The main mathematical tool is a new characterization of continuously differentiable strictly convex functions. We first describe this characterization, and then explain how it can be applied to the calculus of variations and to elastostatics.

(Received September 17 1979)

Footnotes

* On leave from Heriot-Watt University, Edinburgh EH14 4AS. Research partially supported by U.S. Army Contract no. DAAG29-79-C-0086.