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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Examples of capacity for some elliptic operators


Author: Jang-Mei Wu
Journal: Trans. Amer. Math. Soc. 333 (1992), 379-395
MSC: Primary 35J15; Secondary 31B15, 31B35
DOI: https://doi.org/10.1090/S0002-9947-1992-1062196-0
MathSciNet review: 1062196
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Abstract: We study $ L$-capacities for uniformly elliptic operators of nondivergence form

$\displaystyle L = \sum\limits_{i,j} {{a_{ij}}(x)\frac{{{\partial ^2}}} {{\parti... ...rtial {x_j}}} + } \sum\limits_j {{a_j}(x)\frac{\partial } {{\partial {x_j}}};} $

and construct examples of large sets having zero $ L$-capacity for some $ L$ , and small sets having positive $ L$-capacity. The relations between ellipticity constants of the coefficients and the sizes of these sets are also considered.

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DOI: https://doi.org/10.1090/S0002-9947-1992-1062196-0
Article copyright: © Copyright 1992 American Mathematical Society