On local regularity estimates for fractional powers of parabolic operators with time-dependent measurable coefficients
On local regularity estimates for fractional powers of parabolic operators with time-dependent measurable coefficients
Abstract We consider fractional operators of the form $$\begin{aligned} {\mathcal {H}}^s=(\partial _t -\text {div}_{x} ( A(x,t)\nabla _{x}))^s,\ (x,t)\in {\mathbb {R}}^n\times {\mathbb {R}}, \end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>∂</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mtext>div</mml:mtext> <mml:mi>x</mml:mi> </mml:msub> <mml:mrow> …