An a priori estimate in the calculus of variations

Steven C. Pinault

Vol. 112 (1984), No. 2, 427–430

DOI: 10.2140/pjm.1984.112.427

Abstract

This work is concerned with establishing an a priori estimate for the tilt excess of a k-dimensional varifold in Rⁿ which is stationary with respect to the integral of a positive elliptic parametric integrand. For such a varifold, the tilt excess with respect to any k-plane T is estimated a priori by the integral square deviation of the varifold from T. This estimate is applied in the author’s Ph. D. thesis, in the case of a C² two dimensional graph in Rⁿ to derive an a priori pointwise bound on the slope.

Mathematical Subject Classification

Primary: 49F22, 49F22

Milestones

Received: 14 June 1982

Published: 1 June 1984