We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.

Lipschitz Bounds and Nonautonomous Integrals / De Filippis, C.; Mingione, G.. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 242:2(2021), pp. 973-1057. [10.1007/s00205-021-01698-5]

Lipschitz Bounds and Nonautonomous Integrals

De Filippis C.;Mingione G.
2021-01-01

Abstract

We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.
Lipschitz Bounds and Nonautonomous Integrals / De Filippis, C.; Mingione, G.. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 242:2(2021), pp. 973-1057. [10.1007/s00205-021-01698-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2902784
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