Resolvent estimates in W−1,p related to strongly coupled‐linear parabolic systems with coupled nonsmooth capacities
Annegret Glitzky, Rolf Hünlich · Mathematical Methods in the Applied Sciences · 2007
Abstract We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W−1, p spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain Lp estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd.