A simple partial regularity proof for minimizers of variational integrals

Schmidt T (2009)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2009

Journal

Nodea-Nonlinear Differential Equations and Applications Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 16

Pages Range: 109-129

Journal Issue: 1

URI: http://cvgmt.sns.it/paper/1768/

DOI: 10.1007/s00030-008-8012-1

Abstract

We consider multi-dimensional variational integrals F[u] := ∫Omega; f(·, u, Du) dx for u : ℝⁿ⊃ Ω→ ℝ^N, where the integrand f is a strictly convex function of its last argument. We give an elementary proof for the partial C¹α -regularity of minimizers of F. Our approach is based on the method of A-harmonic approximation, avoids the use of Gehring's lemma, and establishes partial regularity with the optimal Hölder exponent α in a single step. © 2009 Birkhaueser.

Authors with CRIS profile

Thomas Schmidt Department Mathematik

How to cite

APA:

Schmidt, T. (2009). A simple partial regularity proof for minimizers of variational integrals. Nodea-Nonlinear Differential Equations and Applications, 16(1), 109-129. https://dx.doi.org/10.1007/s00030-008-8012-1

MLA:

Schmidt, Thomas. "A simple partial regularity proof for minimizers of variational integrals." Nodea-Nonlinear Differential Equations and Applications 16.1 (2009): 109-129.

BibTeX: Download