On solvability of parabolic equations with singular coefficients in odd mixed-norm Morrey-Sobolev spaces

Abstract

We prove an existence and uniqueness theorem for second-order parabolic equations in the whole space with constant zeroth-order coefficient in mixed-norm Morrey-Sobolev spaces. The main coefficient $a$ is assumed to be measurable in $t$ and BMO in $x$ and the first-order coefficients $b$ are in an appropriate mixed-norm Morrey classes (thus admitting rather rough singularities). The mixed-norm Morrey-Sobolev spaces are ``odd'' in the sense that the interior integration in the formula defining the norm is performed with respect to $t$ and not to $x$ as is customary.