Higher differentiability of minimizers of variational integrals with Sobolev coefficients
Abstract.
In this paper we consider integral functionals of the form
with convex integrand satisfying p growth conditions with respect to the gradient variable. As a novel feature, the dependence of the integrand on the x-variable is allowed to be through a Sobolev function. We prove local higher differentiability results for local minimizers of the functional 𝔉, establishing uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand. Furthermore, we prove a dimension free higher integrability result for the gradient of local minimizers, by the use of a weighted version of the Gagliardo–Nirenberg interpolation inequality.
© 2014 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- n/p-harmonic maps: Regularity for the sphere case
- On the structure of minimizers of causal variational principles in the non-compact and equivariant settings
- Higher differentiability of minimizers of variational integrals with Sobolev coefficients
- A second derivative Hölder estimate for weak mean curvature flow
Articles in the same Issue
- Masthead
- n/p-harmonic maps: Regularity for the sphere case
- On the structure of minimizers of causal variational principles in the non-compact and equivariant settings
- Higher differentiability of minimizers of variational integrals with Sobolev coefficients
- A second derivative Hölder estimate for weak mean curvature flow
