MMN-765
Gradient estimates in Morrey spaces of weak solutions to quasilinear parabolic systems of Hörmander's vector fields
Abstract
This paper is concerned with higher integrability for gradients of weak solutions to
quasilinear parabolic systems of H ̈ rmander’s vector fields. We establish Lp estimates for gradi-
o
ents of weak solutions by deriving a parabolic Caccioppli inequality and using the reverse H ̈ lder
o
inequality in parabolic cylinders, and then obtain Lp estimates for gradients of weak solutions
to homogeneous parabolic system. At last higher integrability of gradients in Morrey space with
p 2 is proved.
Vol. 14 (2013), No. 3, pp. 851-869