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arXiv · 2203.03482

Borderline Lipschitz regularity for bounded minimizers of functionals with (p,q)-growth

Karthik Adimurthi·Vivek Tewary
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Abstract

We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard $p,q$-growth with the source term in the Lorentz space $L(N,1)$ under the restriction $q<p+1+p\,\min\left\{\frac 1N,\frac{2(p-1)}{Np-2p+2}\right\}$. This extends the recent work by Beck-Mingione to bounded minimizers under weaker hypothesis and is sharp for some special ranges of $p$, $q$ and $N$.

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Karthik Adimurthi, Vivek Tewary. 2022-03-07. Borderline Lipschitz regularity for bounded minimizers of functionals with (p,q)-growth. https://arxiv.org/abs/2203.03482

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