Existence of boundary values for metaharmonic functions
Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1417-1448
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Necessary and sufficient conditions for the existence of $L_2$-limits at the boundary of solutions of a metaharmonic equation in a half-space are established. In the case of Laplace's equation these criteria coincide with Riesz's theorem: a harmonic function has an $L_2$-limit at the boundary if and only if it is $L_2$-bounded.
@article{SM_1999_190_10_a1,
author = {V. P. Mikhailov},
title = {Existence of boundary values for metaharmonic functions},
journal = {Sbornik. Mathematics},
pages = {1417--1448},
year = {1999},
volume = {190},
number = {10},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1999_190_10_a1/}
}
V. P. Mikhailov. Existence of boundary values for metaharmonic functions. Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1417-1448. http://geodesic.mathdoc.fr/item/SM_1999_190_10_a1/
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