WIAS Preprint No. 1086, (2006)

Resolvent estimates in $W^-1,p$ related to strongly coupled linear parabolic systems with coupled nonsmooth capacities



Authors

  • Glitzky, Annegret
  • Hünlich, Rolf

2010 Mathematics Subject Classification

  • 35K45 35R05 35B65

Keywords

  • Linear parabolic systems, coupled capacities, strong coupling, nonsmooth data, resolvent estimates, regularity, existence, uniqueness

DOI

10.20347/WIAS.PREPRINT.1086

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 $L^p$ estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result.

Appeared in

  • Math. Methods Appl. Sci., 30 (2007) pp. 2215--2232.

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