Parabolic p-systems: Hölder continuity of Du

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


The space gradient Du of local weak solutions of the quasilinear system (1.10) of Chap. VIII are locally Holder continuous in Ω T provided the structure conditions (Si)-(S6) are in force. We will show this first for the homogeneous system (1.1) and then will indicate how to extend it to the general systems (1.10). The estimates of this chapter hold in the interior of 12T and deteriorate near its parabolic boundary T. If K is a compact subset ofΩ T we let dist (К; Γ) denote the parabolic distance from К to the parabolic boundaryΓof Ω T,i.e., dist
$$ \left( {\mathcal{K};\Gamma } \right) \equiv \mathop {\mathop {\inf }\limits_{\left( {x,t} \right) \in \mathcal{K}} }\limits_{\left( {y,s} \right) \in \Gamma } \left( {\left| {x - y} \right| + \sqrt {\left| {t - s} \right|} } \right) $$


Constant Vector Cutoff Function Singular Case Integral Average Parabolic Boundary 
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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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