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A Note on L p Estimates for Parabolic Systems in Lipschitz Cylinders

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Book cover Partial Differential Equations with Minimal Smoothness and Applications

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 42))

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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.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA

    Russell M. Brown

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Zhongwei Shen

Authors
  1. Russell M. Brown
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  2. Zhongwei Shen
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29303, USA

    B. Dahlberg

  2. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    R. Fefferman , Carlos Kenig  & J. Pipher ,  & 

  3. Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Eugene Fabes

  4. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    David Jerison

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© 1992 Springer-Verlag New York, Inc.

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Brown, R.M., Shen, Z. (1992). A Note on L p Estimates for Parabolic Systems in Lipschitz Cylinders. In: Dahlberg, B., Fefferman, R., Kenig, C., Fabes, E., Jerison, D., Pipher, J. (eds) Partial Differential Equations with Minimal Smoothness and Applications. The IMA Volumes in Mathematics and its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2898-1_9

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  • DOI: https://doi.org/10.1007/978-1-4612-2898-1_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7712-5

  • Online ISBN: 978-1-4612-2898-1

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