Kolmogorov operator with the vector field in Nash class

2020/12/04 by Damir Kinzebulatov, Kinzebulatov, D., Yu. A. Semënov +1
Mathematics · #Differential Equations and Boundary Problems #Numerical methods in inverse problems #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2012.02843

Abstract

We consider divergence-form parabolic equation with measurable uniformly elliptic matrix and the vector field in a large class containing, in particular, the vector fields in L^p, p>d, as well as some vector fields that are not even in L_{\rm loc}^2+ε, ε>0. We establish Hölder continuity of the bounded soutions, sharp two-sided Gaussian bound on the heat kernel, Harnack inequality.

Citations

• A new proof of Moser's parabolic harnack inequality using the old ideas of Nash

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• Regularity for parabolic equations with singular non-zero divergence vector fields