Journal
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
Volume 28, Issue 3, Pages 395-411Publisher
GAUTHIER-VILLARS/EDITIONS ELSEVIER
DOI: 10.1016/j.anihpc.2011.02.005
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Funding
- EPSRC [EP/E035027/1]
- ERC [207573]
- Oxford Centre for Nonlinear Partial Differential Equations
- Dept. Maths. 'R. Caccioppoli' in Napoli
- EPSRC [EP/E035027/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E035027/1] Funding Source: researchfish
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In this paper we consider integral functionals of the form F(nu, Omega) = integral(Omega) F(D nu(x))dx with convex integrand satisfying (p, q) growth conditions. We prove local higher differentiability results for bounded minimizers of the functional F under dimension-free conditions on the gap between the growth and the coercivity exponents. As a novel feature, the main results are achieved through uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand. (C) 2011 Elsevier Masson SAS. All rights reserved.
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