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We obtain Lipschitz estimates for bounded minimizers of functionals withnonstandard $(p,q)$-growth satisfying the dimension-independent restriction$q<p+2$ with $p \geq 2$. This relation improves existing restrictions when $p\leq N-1$, moreover our result is sharp in the range $N > \frac{p(2+p)}{2} +1$. The standard Lipschitz regularity takes the form $W^{1,\infty}_{\text{loc}}- W^{1,p}_{\text{loc}}$, whereas we obtain $W^{1,\infty}_{\text{loc}} -L^{\infty}_{\text{loc}}$ regularity estimate and then make use of existingsharp $L^{\infty}_{\text{loc}}$ bounds to obtain the required conclusion.

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