Lipschitz bounds for nonuniformly elliptic integral functionals in the plane (Q6621284)

In this short note, the author studies local regularity properties of local minimizer of scalar integral functionals with controlled \((p, q)\)-growth in the two-dimensional plane. Lipschitz continuity for local minimizer is proved under the condition \(1 < p \leq q < +\infty\) with \(q < 3p\) which improve upon the classical results valid in the regime \(q < 2p\). This proof is based upon a \(L^{\infty}-L^2\)-estimate for solutions of linear uniformly elliptic equations in the plane which is optimal.