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Parabolic systems with non continuous coefficients

Pages: 727 - 733, Issue Special, July 2003

 Abstract        Full Text (195.6K)              

Maria Alessandra Ragusa - Dipartimento di Matematica e Informatica, Viale Andrea Doria, 6, 95128- Catania, Italy (email)

Abstract: 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, estimates in Lebesgue spaces, highest order derivatives.
Mathematics Subject Classification:  Primary: 35J30, 35J45, 35B01; Secondary: 35J35.

Received: September 2002;      Revised: March 2003;      Published: April 2003.