Perturbation theory for the parabolic Regularity and Neumann problem

Abstract

We show small and large Carleson perturbation results for the parabolic Regularity boundary value problem with boundary data in ${\dot{L}}_{1,1/2}^p$ and small Carelson perturbation results for the Neumann problem with boundary data in $L^p$. The operator we consider is $L:={\partial }_t-\mathrm{div}(A\nabla \cdot )$ and the domains are parabolic cylinders $\hat{I}\text{c◯}=\mathcal{O}\times \mathbb{R}$, where $\mathcal{O}$ is a Lipschitz domain.