Conormal problem of higher-order parabolic systems

Abstract

The paper is a comprehensive study of the $L_p$ and the Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients in the half space and cylindrical domains with conormal derivative boundary condition. For the $L_p$ estimates, we assume that the leading coefficients are only bounded measurable in the $t$ variable and $VMO$ 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 both variables.

49 pages, submitted

References in corpus (2)

• Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains
• The Schauder estimates for higher-order parabolic systems with time irregular coefficients