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

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 $q<p+1+p\min \left\{\frac{1}{N},\frac{2(p-1)}{Np-2p+2}\right\}$. 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 $N$.

17 pages. arXiv admin note: text overlap with arXiv:2108.06153