On the Local Boundedness of Solutions to the Equation −Δu + a∂_zu = 0

The equation −Δu(z, x′) + a(x′)∂_zu(z, x′) = 0 in an domain of an n-dimensional space is considered. The coefficient at the lower order summand does not depend on the direction in which the derivative is taken. It is established that if a ∈ L_p for p > \(\frac{n-1}{2}\) $\frac{n-1}{2}$ , then the solution u is locally bounded. If p = \(\frac{n-1}{2}\) $\frac{n-1}{2}$ then the solution can be unbounded.