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)


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


Dirichlet Problem NEUMANN Problem Lipschitz Domain Parabolic System Singular Integral Operator 
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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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