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We introduce elliptic and parabolic $\mathcal{B}_{1}$ classes that generalizethe well-known $\mathfrak{B}_{p}$ classes of DeGiorgi, Ladyzhenskaya andUral'tseva with $p>1$. New classes are applied to prove pointwise continuity ofsolutions of elliptic and parabolic equations with nonstandard growthconditions. Our considerations cover new cases of variable exponent and $(p,q)$-phase growth including the ,,singular-degenerate'' parabolic case $p<2<q$.

$\mathcal{B}_{1}$ classes of DeGiorgi-Ladyzhenskaya-Ural'tseva and their  applications to elliptic and parabolic equations with generalized Orlicz  growth conditions