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2003, 2003(Special): 727-733. doi: 10.3934/proc.2003.2003.727

Parabolic systems with non continuous coefficients

Maria Alessandra Ragusa 1,

1. 

Dipartimento di Matematica e Informatica, Viale Andrea Doria, 6, 95128- Catania, Italy

Received  September 2002 Revised  March 2003 Published  April 2003

In this note we are interested in the local regularity of the highest order derivatives of the solutions of the system

$T u = fi(y)$      $i = 1,...,N



where the known terms $f_i$ are in Lebesgue spaces and the differential the parabolic operator $T$ has the form


$ut - \sum_{j=1}^{N}\sum_{|\alpha|=2s} a^(\alpha)_(ij) (y)D^(\alpha) u_j (y) + \sum_{j=1}^{N}\sum_{|\alpha|<=2s-1} b^(\alpha)_(ij) (y)D^(\alpha) u_j (y)$.

have discontinuous coefficients.

Keywords: Parabolic systems, highest order derivatives., estimates in Lebesgue spaces.
Mathematics Subject Classification: Primary: 35J30, 35J45, 35B01; Secondary: 35J3.
Citation: Maria Alessandra Ragusa. Parabolic systems with non continuous coefficients. Conference Publications, 2003, 2003 (Special) : 727-733. doi: 10.3934/proc.2003.2003.727
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