The Dirichlet problem and nondivergence harmonic measure

Author:
Cristian Rios

Journal:
Trans. Amer. Math. Soc. **355** (2003), 665-687

MSC (2000):
Primary 35J25; Secondary 35B20, 31B35

DOI:
https://doi.org/10.1090/S0002-9947-02-03145-8

Published electronically:
October 1, 2002

MathSciNet review:
1932720

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the Dirichlet problem

for two second-order elliptic operators , , in a bounded Lipschitz domain . The coefficients belong to the space of bounded mean oscillation with a suitable small modulus. We assume that is regular in for some , , that is, for all continuous boundary data . Here is the surface measure on and is the nontangential maximal operator. The aim of this paper is to establish sufficient conditions on the difference of the coefficients that will assure the perturbed operator to be regular in for some , .

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Additional Information

**Cristian Rios**

Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Address at time of publication:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8R-B19 Canada

Email:
riosc@math.mcmaster.ca

DOI:
https://doi.org/10.1090/S0002-9947-02-03145-8

Keywords:
Nondivergence elliptic equations,
Dirichlet problem,
harmonic measure

Received by editor(s):
April 5, 2002

Received by editor(s) in revised form:
May 17, 2002

Published electronically:
October 1, 2002

Dedicated:
In memory of E. Fabes

Article copyright:
© Copyright 2002
American Mathematical Society