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

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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