A simple partial regularity proof for minimizers of variational integrals - Schmidt, Thomas (Nodea-Nonlinear Differential Equations and Applications, 2009)
We consider multi-dimensional variational integrals F[u] := ∫Omega; f(·, u, Du) dx for u : ℝn⊃ Ω→ ℝN, 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.
UnivIS-Import:2015-03-09:Pub.2009.nat.dma.lma2.asimpl
Keywords: Minimizer; Partial regularity; Variational integral