The cauchy-dirichlet problem for parabolic equations with VMO coefficients

In this note, we prove the well posedness for a Cauchy-Dirichlet problem in the class W1,2p, for every p between 1 and ∞. in part of the linear parabolic operator is symmetric, uniformly elliptic and belongs to the Sarasonʹs class VMO. uently, we prove a boundary estimate of the solution u, where the related constant depends on coefficients only through the ellipticity constant and the VMO moduli.