Partial regularity for non autonomous functionals with non standard growth conditions |
| |
Authors: | Bruno De Maria Antonia Passarelli di Napoli |
| |
Institution: | 1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico, II”, via Cintia, Napoli, 80126, Italy
|
| |
Abstract: | We prove a C 1,μ partial regularity result for minimizers of a non autonomous integral funcitional of the form $$\mathcal{F}(u; \Omega):=\int_{\Omega}f(x, Du)\ dx$$ under the so-called non standard growth conditions. More precisely we assume that $$c |z|^{p}\leq f(x ,z) \leq L (1+|z|^{q}),$$ for 2 ≤ p < q and that D z f(x, z) is α-Hölder continuous with respect to the x-variable. The regularity is obtained imposing that ${\frac{p}{q} < \frac{n+\alpha}{n}}$ but without any assumption on the growth of ${D^{2}_{z}f}$ . |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|