Interior Calderón-Zygmund estimates for solutions to general parabolic equations of p-Laplacian type

2017/09/08 by Truyen Nguyen, Nguyen, Truyen
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1709.02847

Abstract

We study general parabolic equations of the form u_t = div A(x,t, u,D u) + div(|F|^p-2 F)+ f whose principal part depends on the solution itself. The vector field A is assumed to have small mean oscillation in x, measurable in t, Lipschitz continuous in u, and its growth in Du is like the p-Laplace operator. We establish interior Calderón-Zygmund estimates for locally bounded weak solutions to the equations when p>2n/(n+2). This is achieved by employing a perturbation method together with developing a two-parameter technique and a new compactness argument. We also make crucial use of the intrinsic geometry method by DiBenedetto \citeD2 and the maximal function free approach by Acerbi and Mingione \citeAM.

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