On the regularity of solutions to the equation - \Delta u + b \nabla u = 0

TL;DR

This paper investigates how the local regularity of solutions to the PDE -Δu + b∇u = 0 depends on the properties of the coefficient b, providing insights into the regularity theory for this class of equations.

Contribution

It analyzes the relationship between the coefficient b and the regularity of solutions, offering new theoretical understanding of this PDE.

Findings

Regularity of solutions varies with properties of b

Conditions on b influence solution smoothness

Theoretical results on solution behavior

Abstract

We consider the equation - \Delta u + b \nabla u = 0. The dependence of the local regularity of a solution on the properties of the coefficient b is investigated.