The Dirichlet problem for radially homogeneous elliptic operators

Bass, Richard F.

doi:10.1090/S0002-9947-1990-0968415-9

The Dirichlet problem for radially homogeneous elliptic operators
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by Richard F. Bass

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

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

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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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