The W-(p,q)(1,2)-solvability for a class of fully nonlinear parabolic equations

摘要

The solvability in the Sobolev-Lorentz spaces W-(p,q)(1,2) (Omega(T)) with p > d + 1 and q > 0 is proved for a class of fully nonlinear parabolic equations with small BMO nonlinearities in (x, t)-variables over a bounded parabolic domain with C-1,C-1-smooth lateral boundary. Here, we make use of the unified approach based on the Fefferman-Stein theorem in accordance with almost all pointwise estimate of the sharp functions to establish the estimates of D(2)u and D(t)u in the framework of Lorentz spaces.