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.
Cupini G., Focardi M., Leonetti F., Mascolo E. (2020). On the Hölder continuity for a class of vectorial problems. ADVANCES IN NONLINEAR ANALYSIS, 9(1), 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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