We consider a regular oblique derivative problem for a linear parabolic operator P with VMO principal coefficients. Its unique strong solvability is proved in [15], when Pu epsilon L-p(Q(T)). Our goal here is to show that the solution belongs to the parabolic Morrey space W-p,lambda(2,1) (Q(T)), when Pu epsilon L-p,L-lambda(Q(T)), p epsilon (1, infinity), lambda epsilon (0, n + 2), and Q(T) is a cylinder in R-+(n+1). The a priori estimates of the solution are derived through L-p,L-lambda estimates for singular and nonsingular integral operators.
Morrey regularity of strong solutions to parabolic equations with VMO coefficients
SOFTOVA PALACHEVA, Lyoubomira
2001-01-01
Abstract
We consider a regular oblique derivative problem for a linear parabolic operator P with VMO principal coefficients. Its unique strong solvability is proved in [15], when Pu epsilon L-p(Q(T)). Our goal here is to show that the solution belongs to the parabolic Morrey space W-p,lambda(2,1) (Q(T)), when Pu epsilon L-p,L-lambda(Q(T)), p epsilon (1, infinity), lambda epsilon (0, n + 2), and Q(T) is a cylinder in R-+(n+1). The a priori estimates of the solution are derived through L-p,L-lambda estimates for singular and nonsingular integral operators.File in questo prodotto:
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