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arXiv · 2409.08796

Regularity results for minimizers of non-autonomous integral functionals

Antonio Giuseppe Grimaldi·Stefania Russo
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Abstract

We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{equation} \mathcal{F}(u,\Omega):=\int_\Omega \left[ f(x,Du)- g \cdot u \right] dx , \notag \end{equation} under $(p,q)$-growth conditions. Besides a suitable differentiability assumption on the partial map $x \mapsto D_\xi f(x,\xi)$, we do not need to assume any differentiability assumption on the function $g$. Moreover, we show that the higher differentiability result holds true also assuming strict convexity and growth conditions on $f$ only at infinity.

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Antonio Giuseppe Grimaldi, Stefania Russo. 2024-09-13. Regularity results for minimizers of non-autonomous integral functionals. https://arxiv.org/abs/2409.08796

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