The Dirichlet problem for radially homogeneous elliptic operators

Author:
Richard F. Bass

Journal:
Trans. Amer. Math. Soc. **320** (1990), 593-614

MSC:
Primary 35J25; Secondary 35B50, 60J60

MathSciNet review:
968415

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Abstract | References | Similar Articles | Additional Information

Abstract: The Dirichlet problem in the unit ball is considered for the strictly elliptic operator , where the , are smooth away from the origin and radially homogeneous: . Existence and uniqueness are proved for solutions in a certain space of functions. Necessary and sufficient conditions are given for an extended maximum principle to hold.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1990-0968415-9

Keywords:
Dirichlet problem,
maximum principle,
elliptic operator,
radially homogeneous,
diffusion processes,
martingale problem

Article copyright:
© Copyright 1990
American Mathematical Society