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The Regularity of Critical Points of Polyconvex Functionals

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Abstract.

In this paper we are concerned with the question of regularity of critical points for functionals of the type eq1 We construct a smooth, strongly polyconvex eq2, and Lipschitzian weak solutions eq3 to the corresponding Euler-Lagrange system, which are nowhere C 1. Moreover we show that F can be chosen in such a way that these irregular weak solutions are weak local minimisers.

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  1. Institute for Advanced Study, School of Mathemetics Princeton, NJ 08540, U.S.A

    László Székelyhidi, Jr.

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  1. László Székelyhidi, Jr.
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Székelyhidi, Jr., L. The Regularity of Critical Points of Polyconvex Functionals. Arch. Rational Mech. Anal. 172, 133–152 (2004). https://doi.org/10.1007/s00205-003-0300-7

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