Pressure Gradient One Sided Cell #
Part of the Caffarelli–Kohn–Nirenberg partial regularity proof.
Origin used for the normalized pressure-gradient estimate.
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The cell is carried by the inner half of a symmetric parabolic ball.
Componentwise Morrey-cell bound for the gradient restricted to a smaller parabolic ball.
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- One or more equations did not get rendered due to their size.
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The old origin carrier is a consequence of the free-centre carrier.
The carrier of the pressure-gradient estimate is the backward cylinder about
the origin, not the symmetric parabolic ball of eq:pressure-gradient-morrey.
The hypothesis of thm:A is closure (parabolicCylinder 0 0 1) ⊆ spaceTimeSet Ω I,
and a symmetric parabolic ball about any point contains times strictly after
that point, so no symmetric ball about the origin is known to lie in the
domain. oneSidedPressureGradientOriginCellOutput is therefore the cell form
of eq:pressure-gradient-morrey with the indicator of that backward
cylinder; the Morrey seminorm is recovered as the supremum of the cells.
Componentwise Morrey-cell bound for the gradient restricted to the normalized cylinder.
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- One or more equations did not get rendered due to their size.