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A Note on Lp Estimates for Parabolic Systems in Lipschitz Cylinders

  • Russell M. Brown
  • Zhongwei Shen
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 42)

Abstract

Let Ω be a bounded Lipschitz domain in R n. Consider the parabolic system
$$\frac{\partial\vec{u}}{\partial t} = \mu\Delta \vec{u} + (\lambda +\mu)\bigtriangledown (\text{div}\vec{u}) \ \ \text{in} \ \ \Omega_T = \Omega \times(0,T)$$
(1)
where 0<T<∞, μ > 0 and λ < −2μ/n are constants.

Keywords

Dirichlet Problem NEUMANN Problem Lipschitz Domain Parabolic System Singular Integral Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Russell M. Brown
    • 1
  • Zhongwei Shen
    • 2
  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

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