A boundary regularity result for minimizers of variational integrals with nonstandard growth
Abstract
We prove global Lipschitz regularity for a wide class of convex variational integrals among all functions in $W^{1,1}$ with prescribed (sufficiently regular) boundary values, which are not assumed to satisfy any geometrical constraint (as for example bounded slope condition). Furthermore, we do not assume any restrictive assumption on the geometry of the domain and the result is valid for all sufficiently smooth domains. The result is achieved with a suitable approximation of the functional together with a new construction of appropriate barrier functions.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2018
- DOI:
- 10.48550/arXiv.1802.09934
- arXiv:
- arXiv:1802.09934
- Bibcode:
- 2018arXiv180209934B
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Primary: 35J47;
- Secondary: 35J25
- E-Print:
- arXiv admin note: text overlap with arXiv:1310.6845 by other authors