Abstract.
We consider multi-dimensional variational integrals
where the integrand f is a strictly convex function of its last argument. We give an elementary proof for the partial \(C^{1,\alpha}\)-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.
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Schmidt, T. A Simple Partial Regularity Proof for Minimizers of Variational Integrals. Nonlinear differ. equ. appl. 16, 109–129 (2009). https://doi.org/10.1007/s00030-008-8012-1
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DOI: https://doi.org/10.1007/s00030-008-8012-1