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arXiv · 1911.12822

Growth conditions and regularity, an optimal local boundedness result

Jonas Hirsch·Mathias Schäffner
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Abstract

We prove local boundedness of local minimizers of scalar integral functionals $\int_\Omega f(x,\nabla u(x))\,dx$, $\Omega\subset\mathbb R^n$ where the integrand satisfies $(p,q)$-growth of the form \begin{equation*} |z|^p\lesssim f(x,z)\lesssim |z|^q+1 \end{equation*} under the optimal relation $\frac1p-\frac1q\leq \frac1{n-1}$.

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Jonas Hirsch, Mathias Schäffner. 2019-11-28. Growth conditions and regularity, an optimal local boundedness result. https://arxiv.org/abs/1911.12822

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