Accepted Paper

Inserted: 31 jul 2026
Last Updated: 31 jul 2026

Journal: Annali di Matematica Pura ed Applicata
Volume: 195
Number: (5)
Pages: 1575–1603
Year: 2016
Doi: 10.1007/s10231-015-0529-4

Abstract:

In the general vector-valued case $N \ge 1$ we prove the Lipschitz-continuity of local minimizers to some integrals of the Calculus of Variations of the form $ \int_{\Omega} g(x,
Du
)\,dx$, with $p,q-$growth conditions only for $
Du
\rightarrow +\infty$ and without further structure conditions on the integrand $g=g(x,
Du
)$. We apply the regularity results to weak solutions to nonlinear elliptic systems of the form $\sum_{i=1}^{n}\frac{\partial }{\partial x_{i}}a_{i}^{\alpha }\left( x,Du\right) =0$, $\alpha =1,2,\ldots ,N$.

Download:

• EMM-Annali-15-7-24.pdf