Estimates on the solution of an elliptic equation related to Brownian motion with drift. II
type: Item
instance of: scholarly article
title: Estimates on the solution of an elliptic equation related to Brownian motion with drift. II
zbMATH Open document ID: 0899.35029
DOI: 10.4171/RMI/231
author: Joseph G. Conlon
author: Peder A. Olsen
published in: Revista Matemática Iberoamericana
publication date: 1998-11-17T00:00:00Z
full work available at URL: https://eudml.org/doc/39535
review text: 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.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 1136593
zbMATH Keywords: Laplace equation with drift
zbMATH Keywords: Morrey space
zbMATH Keywords: existence
reviewed by: Niels Jacob
MaRDI profile type: Publication
OpenAlex ID: W2085018523
description: scientific article; zbMATH DE number 1136593