We deal with linear parabolic (in the sense of Petrovskii) systems of order 2b with discontinuous principal coefficients. A priori estimates in Sobolev and Sobolev-Morrey spaces are proved for the strong solutions by means of potential analysis and boundedness of certain singular integral operators with kernels of mixed homogeneity. As a byproduct, precise characterization of the Morrey, BMO and Holder regularity is given for the solutions and their derivatives up to order 2b - 1.

A priori estimates and precise regularity for parabolic systems with discontinuous data

SOFTOVA PALAGACHEVA, Lyoubomira
2005

Abstract

We deal with linear parabolic (in the sense of Petrovskii) systems of order 2b with discontinuous principal coefficients. A priori estimates in Sobolev and Sobolev-Morrey spaces are proved for the strong solutions by means of potential analysis and boundedness of certain singular integral operators with kernels of mixed homogeneity. As a byproduct, precise characterization of the Morrey, BMO and Holder regularity is given for the solutions and their derivatives up to order 2b - 1.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/220269
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
  • ???jsp.display-item.citation.isi??? 28
social impact