Higher differentiability of minimizers of convex variational integrals
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 3, p. 395-411

In this paper we consider integral functionals of the form $𝔉\left(v,\Omega \right)=\underset{\Omega }{\int }F\left(Dv\left(x\right)\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$ with convex integrand satisfying $\left(p,q\right)$ 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.

⇒ corrected-by Erratum
DOI : https://doi.org/10.1016/j.anihpc.2011.02.005
Classification:  49N15,  49N60,  49N99
@article{AIHPC_2011__28_3_395_0,
author = {Carozza, Menita and Kristensen, Jan and Passarelli di Napoli, Antonia},
title = {Higher differentiability of minimizers of convex variational integrals},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {28},
number = {3},
year = {2011},
pages = {395-411},
doi = {10.1016/j.anihpc.2011.02.005},
zbl = {1245.49052},
mrnumber = {2795713},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2011__28_3_395_0}
}

Carozza, Menita; Kristensen, Jan; Passarelli di Napoli, Antonia. Higher differentiability of minimizers of convex variational integrals. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 3, pp. 395-411. doi : 10.1016/j.anihpc.2011.02.005. http://www.numdam.org/item/AIHPC_2011__28_3_395_0/

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