Estimates on the solution of an elliptic equation related to Brownian motion with drift. II
This paper continues the paper of \textit{J. Conlon} and \textit{J. Redondo} [Rev. Mat. Iberoam. 11, 1-65 (1995; Zbl 0828.35037)]. In the paper under review the authors discuss the Dirichlet problem \[ (-\Delta- b(x)\cdot \nabla) n(x)=f\quad \text{in }B_R(0) \subset \mathbb{R}^3, \quad u(x)= 0\quad\text{on }\partial B_R (0) \] where the drift vector field \(b:\mathbb{R}^3 \to \mathbb{R}^3\) and the right hand side \(f\) belong to certain Morrey spaces \(M^q_r(\mathbb{R}^3)\). In particular the authors give an existence result for uniformly Hölder continuous solutions, and estimates for the solution \(u\) in the sup-norm with precise dependence on \(R\) and the norm of \(f\) in Morrey spaces.
scientific article; zbMATH DE number 1136593