1993 | OriginalPaper | Chapter
Parabolic p-systems: Hölder continuity of D u
Author : Emmanuele DiBenedetto
Published in: Degenerate Parabolic Equations
Publisher: Springer New York
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
The space gradient Du of local weak solutions of the quasilinear system (1.10) of Chap. VIII are locally Holder continuous in ΩT 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 ofΩT we let dist (К; Γ) denote the parabolic distance from К to the parabolic boundaryΓof ΩT,i.e., dist$$ \left( {\mathcal{K};\Gamma } \right) \equiv \mathop {\mathop {\inf }\limits_{\left( {x,t} \right) \in \mathcal{K}} }\limits_{\left( {y,s} \right) \in \Gamma } \left( {\left| {x - y} \right| + \sqrt {\left| {t - s} \right|} } \right) $$