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

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 different...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2007-11, Vol.30 (17), p.2215-2232
Main Authors: Glitzky, Annegret, Hünlich, Rolf
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
coupled capacities
Exact sciences and technology
initial value problems for parabolic systems
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Operator theory
Partial differential equations
PDE with discontinuous coefficients or data
regularity
resolvent estimates
Sciences and techniques of general use
strong coupling
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.886