Regularity of minimizers under limit growth conditions

By Giovanni Cupini, Paolo Marcellini, Elvira Mascolo. 2017

57 citations recorded by the source corpus.

Abstract It is well known that an integral of the Calculus of Variations satisfying anisotropic growth conditions may have unbounded minimizers if the growth exponents are too far apart. Under sharp assumptions on the exponents we prove the local boundedness of minimizers of functionals with anisotropic p , q -growth, via the De Giorgi method. As a by-product, regularity of minimizers of some non coercive functionals is obtained by reduction to coercive ones.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7a2cf280ef9e07a9212d64481394b97be54bf771

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Regularity results for vectorial minimizers of a class of degenerate convex integrals (2018, background): “When treating the regularity of minimizers, the proof of their local boundedness can be seen as a first step in the analysis of further regularity properties (see [12], [13] for recent contributions to the (p, q) growth case).”
Lipschitz regularity for orthotropic functionals with nonstandard growth conditions (2018, background): “1] and the papers [11, 12] by Cupini, Marcellini and Mascolo for the case of more general functionals.”
Regularity for general functionals with double phase (2017, result): “3), while further results in this direction can be for instance found in [2, 3, 4, 8, 11, 9, 12, 13, 14, 20, 47, 48, 49, 52]; see also the work of Ragusa & Tachikawa for partial regularity [50, 51, 52].”