Morrey regularity of strong solutions to parabolic equations with VMO coefficients

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∈ L p(Q T) . Our goal here is to show that the solution belongs to the parabolic Morrey space W p, λ 2,1( Q T ), when Pu∈ L p,λ(Q T) , p∈(1,∞), λ∈(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, λ estimates for singular and nonsingular integral operators.