Hölder continuity for vectorial local minimizers of variational integrals
Yanan Shan, Hongya Gao · Rocky Mountain Journal of Mathematics · 2022
This note deals with vectorial local minimizers of some integral functionals related to nonlinear elasticity theory. Under some structural assumptions, we derive that each component of the local minimizers lies in the De Giorgi class, thus the minimizers are locally Hölder continuous. We emphasize that no convexity is assumed. On the other hand, a special dependence on minors, taken from the Jacobian matrix, plays an important role in the proof.