In this paper we establish \emph{a priori} $h^1$-estimates in a bounded domain for parabolic equations with vanishing $\operatorname{LMO}$ coefficients.

Keywords:

parabolic operator, Hardy space, parabolic, singular integrals and commutators parabolic operator, Hardy space, parabolic, singular integrals and commutators

MSC Classifications:

35K20, 35B65, 35R05 show english descriptions Initial-boundary value problems for second-order parabolic equations
Smoothness and regularity of solutions
Partial differential equations with discontinuous coefficients or data 35K20 - Initial-boundary value problems for second-order parabolic equations
35B65 - Smoothness and regularity of solutions
35R05 - Partial differential equations with discontinuous coefficients or data

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