Document Type
Article
Date
9-4-2011
Disciplines
Mathematics
Description/Abstract
We obtain Lipschitz regularity results for a fairly general class of nonlinear first-order PDEs. 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 relay 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-Hookian type problems.
Recommended Citation
Iwaniec, Tadeusz; Kovalev, Leonid V.; and Onninen, Jani, "Lipschitz Regularity for Inner-Variational Equations" (2011). Mathematics - All Scholarship. 47.
https://surface.syr.edu/mat/47
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1109.0720