An <inline-formula><tex-math id="M1">\begin{document} $L_p$\end{document}</tex-math></inline-formula>-Lipschitz theory for parabolic equations with time measurable pseudo-differential operators
An <inline-formula><tex-math id="M1">\begin{document} $L_p$\end{document}</tex-math></inline-formula>-Lipschitz theory for parabolic equations with time measurable pseudo-differential operators
In this article we prove the existence and uniqueness of a (weak) solution $u$ in $L_p\left( (0, T); Λ_{γ+m}\right)$ to the Cauchy problem $\begin{align}\notag&\frac{\partial u}{\partial t}(t, x) = ψ(t, i\nabla)u(t, x)+f(t, x), \;\;\;(t, x) ∈ (0, T) × {\bf{R}}^d \\& u(0, x) = 0, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(1)\end{align}$ where $d ∈ \mathbb{N}$, $p …