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15 March 2013 Lipschitz regularity for inner-variational equations
Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Duke Math. J. 162(4): 643-672 (15 March 2013). DOI: 10.1215/00127094-2079791

Abstract

We obtain Lipschitz regularity results for a fairly general class of nonlinear first-order partial differential equations. These equations arise from the inner variation of certain energy integrals. Even in the simplest model case of the Dirichlet energy the inner-stationary solutions need not be differentiable everywhere; the Lipschitz continuity is the best possible. But the proofs, even in the Dirichlet case, turn out to rely on topological arguments. The appeal to the inner-stationary solutions in this context is motivated by the classical problems of existence and regularity of the energy-minimal deformations in the theory of harmonic mappings and certain mathematical models of nonlinear elasticity, specifically, neo-Hookean-type problems.

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Tadeusz Iwaniec. Leonid V. Kovalev. Jani Onninen. "Lipschitz regularity for inner-variational equations." Duke Math. J. 162 (4) 643 - 672, 15 March 2013. https://doi.org/10.1215/00127094-2079791

Information

Published: 15 March 2013
First available in Project Euclid: 15 March 2013

zbMATH: 1319.49055
MathSciNet: MR3039677
Digital Object Identifier: 10.1215/00127094-2079791

Subjects:
Primary: 49N60
Secondary: 35B65, 73C50

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 4 • 15 March 2013
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