Estimates in Generalized Morrey Spaces for Weak Solutions to Divergence Degenerate Parabolic Systems

2011/09/09 by Dong, Yan, Zhu, Maochun, Niu, Pengcheng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.1929

Abstract

Let X=(X₁,...,X_q) be a family of real smooth vector fields satisfying Hömander's condition. The purpose of this paper is to establish gradient estimates in generalized Morrey spaces for weak solutions of the divergence degenerate parabolic system related to X :%u_tⁱ+X_α^∗(a_ij^αβ(z)X_βu^j%)=g_i+X_α^∗f_i^α(z), where α,β=1,2,...,q, i,j=1,2,...,N, X_α^∗ is the transposed vector field of X_α, z=(t,x)∈ℝⁿ⁺¹, and coefficients a_ij^αβ(z) belong to the space VMO induced by the vector fields X₁, ...,X_q.

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