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Gradient estimates in Morrey spaces of weak solutions to quasilinear parabolic systems of Hörmander’s vector fields. (English) Zbl 1299.35154

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
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