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- Title
Lipschitz Bounds and Nonautonomous Integrals.
- Authors
De Filippis, Cristiana; Mingione, Giuseppe
- Abstract
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.
- Subjects
INTEGRALS; POLYNOMIALS; CLASSIFICATION; VARIATIONAL approach (Mathematics); FUNCTIONALS
- Publication
Archive for Rational Mechanics & Analysis, 2021, Vol 242, Issue 2, p973
- ISSN
0003-9527
- Publication type
Article
- DOI
10.1007/s00205-021-01698-5