Higher differentiability of minimizers of convex variational integrals

Carozza, Menita; Kristensen, Jan; Passarelli di Napoli, Antonia

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 3, pp. 395-411.

In this paper we consider integral functionals of the form

$$𝔉(v,\Omega )=\underset{\Omega }{\int }F\left(Dv\left(x\right)\right)\mathrm{d}x$$

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.

Classification : 49N15, 49N60, 49N99

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