On the heat equation with drift in $L_{d+1}$

Publication date: 31 December 2020

Abstract: In this paper we deal with the heat equation with drift in

L_{d + 1}

. Basically, we prove that, if the free term is in

L_{q}

with high enough

q

, then the equation is uniquely solvable in a rather unusual class of functions such that

p a r t i a l_{t} u, D^{2} u i n L_{p}

with

p < d + 1

and

D u i n L_{q}

.

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