标题： 关于混合局部和非局部拟线性抛物方程的正则性理论 显示英文标题

标题： On the regularity theory for mixed local and nonlocal quasilinear parabolic equations

摘要： 我们考虑混合局部和非局部的拟线性抛物方程，类型为$p$-Laplace，并讨论此类方程弱解的几个正则性性质。 更准确地说，我们建立了弱次解的局部有界性，弱超解的下半连续性以及弱次解的上半连续性。 我们还讨论了半连续代表的逐点行为。 我们的主要结果适用于变号解。 我们的方法是纯粹分析的，基于能量估计和De Giorgi理论。 显示英文摘要

摘要： We consider mixed local and nonlocal quasilinear parabolic equations of $p$-Laplace type and discuss several regularity properties of weak solutions for such equations. More precisely, we establish local boundeness of weak subsolutions, lower semicontinuity of weak supersolutions as well as upper semicontinuity of weak subsolutions. We also discuss the pointwise behavior of the semicontinuous representatives. Our main results are valid for sign changing solutions. Our approach is purely analytic and is based on energy estimates and the De Giorgi theory.