Duke Mathematical Journal
- Duke Math. J.
- Volume 162, Number 4 (2013), 643-672.
Lipschitz regularity for inner-variational equations
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.
Duke Math. J., Volume 162, Number 4 (2013), 643-672.
First available in Project Euclid: 15 March 2013
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Iwaniec, Tadeusz; Kovalev, Leonid V.; Onninen, Jani. Lipschitz regularity for inner-variational equations. Duke Math. J. 162 (2013), no. 4, 643--672. doi:10.1215/00127094-2079791. https://projecteuclid.org/euclid.dmj/1363355690