Calculus of Variations and Geometric Measure Theory
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B. De Maria - A. Passarelli di Napoli

A new partial regularity result for non autonomous convex integrals with non standard growth conditions

created by passarell on 31 May 2010
modified by demaria on 05 May 2011


Published Paper

Inserted: 31 may 2010
Last Updated: 5 may 2011

Journal: J. Differential Equations
Volume: 250
Number: 3
Year: 2011


We establish $C^{1,\gamma}$-partial regularity of minimizers of non autonomous convex integral functionals of the type: $ \mathcal{F}(u; \Omega):=\int_{\Omega}f(x, Du)\ dx , $ with non standard growth conditions into the gradient variable $$ \frac{1}{L}
{p} \leq f(x,\xi) \leq L (1+
{q}) $$ for a couple of exponents $p,q$ such that $$ 1< p\leq q< \min\left\{p \frac{n}{n-1}, p+1\right\} , $$ and $\alpha$- Hölder continuous dependence with respect to the $x$ variable. The significant point here is that the distance between the exponents $p$ and $q$ is independent of $\alpha$. Moreover this bound on the gap between the growth and the coercitivity exponents improves previous results in this setting.


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