Contents Online
Methods and Applications of Analysis
Volume 29 (2022)
Number 2
On the heat equation with drift in $L_{d+1}$
Pages: 195 – 208
DOI: https://dx.doi.org/10.4310/MAA.2022.v29.n2.a3
Author
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 $\partial_t u , D^2 u \in L_p$ with $p \lt d + 1$ and $D_u \in L_q$.
Keywords
heat equation, singular first-order terms, non-perturbative technique
2010 Mathematics Subject Classification
35B45, 35B65
Received 16 March 2021
Accepted 7 January 2022
Published 1 March 2023