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

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{1/N, 2(p - 1)/Np - 2p + 2}. This extends the recent work by Beck and Mingione to bounded minimizers under weaker hypothesis and is sharp for some special ranges of p, q and N.

Automated summary

We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard ( p, q)-growth in the Lorentz space L(N, 1), extending recent work by Beck and Mingione with weaker assumptions. Our result is sharp for certain special ranges of p, q, and N.