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Regularity under sharp anisotropic general growth conditions

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  • We prove boundedness of minimizers of energy-functionals, for instance of the anisotropic type (1) below, under sharp assumptions on the exponents $p_{i}$ in terms of $\overline{p}*$: the Sobolev conjugate exponent of $\overline{p}$; i.e., $\overline{p}*$ = {n\overline{p}}/{n-\overline{p}}, $ $ 1 / \overline{p}$= $\frac{1}{n} \sum_{i=1}^{n}\frac{1}{p_{i}}$. As a consequence, by mean of regularity results due to Lieberman [21], we obtain the local Lipschitz-continuity of minimizers under sharp assumptions on the exponents of anisotropic growth.
    Mathematics Subject Classification: Primary: 49N60; Secondary: 35J70.


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