  We study local regularity properties of local minimizer of scalar integral
functionals with controlled $(p,q)$-growth in the two-dimensional plane. We
establish Lipschitz continuity for local minimizer under the condition $1<p\leq
q<\infty$ with $q<3p$ which improve upon the classical results valid in the
regime $q<2p$. Along the way, we establish an $L^\infty$-$L^2$-estimate for
solutions of linear uniformly elliptic equations in the plane which is optimal
with respect to the ellipticity contrast of the coefficients.
