Conormal problem of higher-order parabolic systems with time irregular coefficients

Dong, Hongjie; Zhang, Hong

doi:10.1090/tran/6605

Conormal problem of higher-order parabolic systems with time irregular coefficients
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by Hongjie Dong and Hong Zhang PDF

Trans. Amer. Math. Soc. 368 (2016), 7413-7460 Request permission

Abstract:

The paper is a comprehensive study of $L_p$ and Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients on a half space and cylindrical domains with the conormal derivative boundary conditions. For the $L_p$ estimates, we assume that the leading coefficients are only bounded and measurable in the $t$ variable and have vanishing mean oscillations (VMO$_x$) with respect to $x$. We also prove the Schauder estimates in two situations: the coefficients are Hölder continuous only in the $x$ variable; the coefficients are Hölder continuous in the $t$ variable as well on the lateral boundary.

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