New pointwise bounds on the fractional gradient of the fractional heat kernel yield global Bessel-potential regularity, a compactness result, and existence for a fractional KPZ equation with nonlocal gradient term.
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Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems
New pointwise bounds on the fractional gradient of the fractional heat kernel yield global Bessel-potential regularity, a compactness result, and existence for a fractional KPZ equation with nonlocal gradient term.