In this paper we prove local Hölder continuity of vectorial local minimizers of special classes of integral functionals with rank-one and polyconvex integrands. The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the Hölder continuity. In the final section, we provide some non-trivial applications of our results.
On the Hölder continuity for a class of vectorial problems / Cupini G.; Focardi M.; Leonetti F.; Mascolo E.. - In: ADVANCES IN NONLINEAR ANALYSIS. - ISSN 2191-9496. - STAMPA. - 9:1(2020), pp. 1008-1025. [10.1515/anona-2020-0039]
On the Hölder continuity for a class of vectorial problems
Cupini G.;
2020
Abstract
In this paper we prove local Hölder continuity of vectorial local minimizers of special classes of integral functionals with rank-one and polyconvex integrands. The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the Hölder continuity. In the final section, we provide some non-trivial applications of our results.| File | Dimensione | Formato | |
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On the Holder continuity for a class of vectorial problems.pdf
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