Higher-order nondivergence elliptic and parabolic equations in Sobolev spaces and Orlicz spaces (Q413198)

In the very interesting paper under review, the authors obtain global regularity estimates in Sobolev and Orlicz spaces for the strong solutions to the Cauchy problem for higher-order parabolic equations of nondivergence form NEWLINE\[NEWLINE u_t-\sum_{|\nu|=0}^{2m} a_\nu(x,t)D^\nu u =f(x,t)\quad \text{in}\;{\mathbb R}^n\times(0,T), NEWLINE\]NEWLINE where the coefficients have small BMO seminorms and satisfy NEWLINE\[NEWLINE (-1)^{m-1} \sum_{|\nu|=2m} a_\nu(x,t)\xi^\nu\geq\Lambda_1|\xi|^{2m},\quad \sum_{|\nu|=0}^{2m} |a_\nu(x,t)|\leq \Lambda_2.NEWLINE\]NEWLINE The corresponding elliptic result is derived as particular case of time-independent data.