Parabolic systems with non continuous coefficients
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.
Received: September 2002; Revised: March 2003; Published: April 2003. |