Vector valued minimizers of anisotropic functionals: fractional differentiability and estimate for the singular set

摘要

We prove “fractional” higher differentiability for the gradient of minimizers of anisotropic integral functionals, if the growth exponents are no too far apart. This allows us to give an estimate for the Hausdorff dimension of the singular set of the minimizers. Mathematics Subject Classification (2000) 49N60 - 35J60 - 35J45