Dong, Yan Gradient estimates in Morrey spaces of weak solutions to quasilinear parabolic systems of Hörmander’s vector fields. (English) Zbl 1299.35154 Miskolc Math. Notes 14, No. 3, 851-869 (2013). Summary: This paper is concerned with higher integrability for gradients of weak solutions to quasilinear parabolic systems of Hörmander’s vector fields. We establish \(L^p\) estimates for gradients of weak solutions by deriving a parabolic Caccioppoli inequality and using the reverse Hölder inequality in parabolic cylinders, and then obtain \(L^p\) estimates for gradients of weak solutions to homogeneous parabolic systems. At last, higher integrability of gradients in Morrey spaces with \(p\geq 2\) is proved. MSC: 35K55 Nonlinear parabolic equations 35B65 Smoothness and regularity of solutions to PDEs Keywords:quasilinear parabolic system; Hörmander vector fields; higher integrability; Caccioppoli inequality; Morrey space; natural condition PDFBibTeX XMLCite \textit{Y. Dong}, Miskolc Math. Notes 14, No. 3, 851--869 (2013; Zbl 1299.35154)