FUNDAMENTALNAYA
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

Abstract

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The Dirichlet and Neumann problems are considered in the $n$-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 $C1,1$ but
narrower that the Hölder space $C1,$a, $0\; <$a <
1.
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
space.

Location: http://mech.math.msu.su/~fpm/eng/k06/k065/k06507h.htm

Last modified: February 21, 2007