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

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In this paper we consider integral functionals of the form

𝔉(v,Ω)=∫ ΩF(Dv(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.

DOI : 10.1016/j.anihpc.2011.02.005
Classification : 49N15, 49N60, 49N99 
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     title = {Higher differentiability of minimizers of convex variational integrals},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {395--411},
     publisher = {Elsevier},
     volume = {28},
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     year = {2011},
     doi = {10.1016/j.anihpc.2011.02.005},
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     zbl = {1245.49052},
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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, Tome 28 (2011) no. 3, pp. 395-411. doi: 10.1016/j.anihpc.2011.02.005

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