Geodesic
On the local boundedness of solutions to the equation $-\Delta u+a\partial_zu=0$
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Tome 508 (2021), pp. 173-184

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Equation $-\Delta u+a\partial_zu=0$ is considered in a domain in $n$-dimensional space. The coefficient in a minor term does not depend on the direction of differentiation in this term. For $a\in L_p$ with $p>\frac{n-1}2$ it is proven that a solution $u$ is locally bounded. If $p=\frac{n-1}2$ then a solution can be unbounded. 
@article{ZNSL_2021_508_a7,
     author = {N. D. Filonov and P. A. Hodunov},
     title = {On the local boundedness of solutions to the equation $-\Delta u+a\partial_zu=0$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {173--184},
     publisher = {mathdoc},
     volume = {508},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_508_a7/}
}
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N. D. Filonov; P. A. Hodunov. On the local boundedness of solutions to the equation $-\Delta u+a\partial_zu=0$. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Tome 508 (2021), pp. 173-184. http://geodesic.mathdoc.fr/item/ZNSL_2021_508_a7/