We prove the local Lipschitz continuity and the higher differentiability of local minimizers of functionals of the form (Formula Presented) with non-autonomous integrand F (x, ζ) which is degenerate convex with respect to the gradient variable. The main novelty here is that the results are obtained assuming that the partial map x → D ζ F (x, ζ) has weak derivative in the almost critical Zygmund class L n log α L and the datum f is assumed to belong to the same Zygmund class.

Very degenerate elliptic equations under almost critical Sobolev regularity / Clop, A.; Giova, R.; Hatami, F.; Passarelli Di Napoli, A.. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 32:6(2020), pp. 1515-1537. [10.1515/forum-2020-0058]

Very degenerate elliptic equations under almost critical Sobolev regularity

Passarelli Di Napoli A.
2020

Abstract

We prove the local Lipschitz continuity and the higher differentiability of local minimizers of functionals of the form (Formula Presented) with non-autonomous integrand F (x, ζ) which is degenerate convex with respect to the gradient variable. The main novelty here is that the results are obtained assuming that the partial map x → D ζ F (x, ζ) has weak derivative in the almost critical Zygmund class L n log α L and the datum f is assumed to belong to the same Zygmund class.
2020
Very degenerate elliptic equations under almost critical Sobolev regularity / Clop, A.; Giova, R.; Hatami, F.; Passarelli Di Napoli, A.. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 32:6(2020), pp. 1515-1537. [10.1515/forum-2020-0058]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/854042
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