Local boundedness of minimizers under unbalanced Orlicz growth conditions

Andrea Cianchi; Mathias Schäffner

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arXiv · 2309.16803

Local boundedness of minimizers under unbalanced Orlicz growth conditions

Andrea Cianchi·Mathias Schäffner

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Abstract

Local minimizers of integral functionals of the calculus of variations are analyzed under growth conditions dictated by different lower and upper bounds for the integrand. Growths of non-necessarily power type are allowed. The local boundedness of the relevant minimizers is established under a suitable balance between the lower and the upper bounds. Classical minimizers, as well as quasi-minimizers are included in our discussion. Functionals subject to so-called $p,q$-growth conditions are embraced as special cases and the corresponding sharp results available in the literature are recovered.

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Andrea Cianchi, Mathias Schäffner. 2023-09-28. Local boundedness of minimizers under unbalanced Orlicz growth conditions. https://arxiv.org/abs/2309.16803

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