论文标题
$ \ MATHCAL {B} _ {1} $类degiorgi-ladyzhenskaya-ural'tseva及其应用于具有广义Orlicz增长条件的椭圆形和抛物线方程
$\mathcal{B}_{1}$ classes of DeGiorgi-Ladyzhenskaya-Ural'tseva and their applications to elliptic and parabolic equations with generalized Orlicz growth conditions
论文作者
论文摘要
我们介绍了椭圆形和抛物线$ \ Mathcal {B} _ {1} $类，这些类概括了众所周知的$ \ Mathfrak {B} _ {p} $ of degiorgi，degiorgi，degiorgi，ladyzhenskaya和uilaltseva，并用$ p> 1 $。新类别用于证明具有非标准生长条件的椭圆形和抛物线方程解的连续性。我们的注意事项涵盖了可变指数的新案例和$（p，q）$ - 阶段增长，包括singular降级的''抛物线案例$ p <2 <q $。
We introduce elliptic and parabolic $\mathcal{B}_{1}$ classes that generalize the well-known $\mathfrak{B}_{p}$ classes of DeGiorgi, Ladyzhenskaya and Ural'tseva with $p>1$. New classes are applied to prove pointwise continuity of solutions of elliptic and parabolic equations with nonstandard growth conditions. Our considerations cover new cases of variable exponent and $(p, q)$-phase growth including the ,,singular-degenerate'' parabolic case $p<2<q$.
