I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2006, VOLUME 12, NUMBER 5, PAGES 75-82
Dirichlet and Neumann problems for Laplace and heat equations in
domains with right angles
A. N. Konenkov
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The Dirichlet and Neumann problems are considered in the -dimensional cube and in
a right angle.
The right-hand side is assumed to be bounded, and the boundary
conditions are assumed to be zero.
We obtain a priori bounds for solutions in the Zygmund space,
which is wider than the Lipschitz space but
narrower that the Hölder space , .
Also, the first and second boundary problems are considered for the
heat equation with similar conditions.
It is shown that the solutions belongs to the corresponding Zygmund
Last modified: February 21, 2007