Vol. 112, No. 2, 1984

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ISSN: 0030-8730
An a priori estimate in the calculus of variations

Steven C. Pinault

Vol. 112 (1984), No. 2, 427–430

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
Received: 14 June 1982
Published: 1 June 1984
Steven C. Pinault