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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
DOI: https://doi.org/10.1090/S0002-9947-1990-0968415-9
MathSciNet review: 968415
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Abstract: The Dirichlet problem in the unit ball is considered for the strictly elliptic operator $ L = \sum {{a_{ij}}{D_{ij}}} $, where the $ {a_{ij}}$, are smooth away from the origin and radially homogeneous: $ {a_{ij}}(rx) = {a_{ij}}(x),\;r > 0,\;x \ne 0$. 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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Additional Information

DOI: https://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

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