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Degenerate and singular parabolic systems

  • Emmanuele DiBenedetto
Part of the Universitext book series (UTX)

Abstract

We turn now to quasilinear systems whose principal part becomes either degenerate or singular at points where. To present a streamlined cross section of the theory, we refer to the model system
$$ \left\{{\begin{array}{*{20}{c}} {u \equiv \left( {{u_1},{u_2}, \ldots,{u_m}} \right),m\in N,}\\ {{u_i}\in{C_{loc}}\left({0,T;L_{loc}^2\left(\Omega\right)}\right)\cap {L^p}\left({0,T;W_{loc}^{1,p}\left(\Omega \right)} \right),i=1,2,\ldots,m,}\\ {{u_t}- div{{\left| {Du}\right|}^{p - 2}}Du =0in{\Omega_{\rm T}}} \end{array}}\right. $$
(1.1)

Keywords

Weak Solution Energy Estimate Elliptic System Degenerate Case Cutoff Function 
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 Science+Business Media New York 1993

Authors and Affiliations

  • Emmanuele DiBenedetto
    • 1
    • 2
  1. 1.Northwestern UniversityUSA
  2. 2.University of Rome IIItaly

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