Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations

We investigate the mixed local and nonlocal parabolic p-Laplace equation $$\begin{aligned} \partial _t u(x,t)-\Delta _p u(x,t)+\mathcal {L}u(x,t)=0, \end{aligned}$$ where $$\Delta _p$$ is usual operator $$\mathcal {L}$$ type operator. Based on combination of suitable Caccioppoli-type inequality Logarithmic Lemma with a De Giorgi–Nash–Moser iteration, we establish boundedness Hölder continuity weak solutions for such equations.