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Inequalities for harmonic functions on spheroids and their applications
Date
2001-06-01
Author
Zahariuta, V
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Hadamard-type interpolational inequalities for norms of harmonic functions are studied for confocal prolate and oblate spheroids. It is shown that the optimal level domains in such inequalities may be non-spheroidal. Moreover, in contrary with the case of analytic functions, there is an unremovable gap between the corresponding optimal level domains for inner and outer versions of Hadamard-type inequalities for harmonic functions. These results are based on some special asymptotical formulas for associated Legendre functions P-n(m), Q(n)(m), when the ratio m/n tends to some number gamma is an element of [0, 1]. The case of spheroids is studied in the frame of the general theory of so-called Lh-functions and extremal Lh-functions (Lh-potentials) (developed earlier by the author), which serves the harmonic functions case much as the theory of plurisubharmonic and maximal plurisubharmonic functions (pluripotentials) (Lelong, Bremermann, Siciak, Zahariuta, Bedford-Taylor, Sadullayev et al.) does in the case of analytic functions of several variables.
Subject Keywords
Sets
URI
https://hdl.handle.net/11511/63753
Journal
INDIANA UNIVERSITY MATHEMATICS JOURNAL
Collections
Department of Mathematics, Article
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V. Zahariuta, “Inequalities for harmonic functions on spheroids and their applications,”
INDIANA UNIVERSITY MATHEMATICS JOURNAL
, pp. 1047–1075, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63753.