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, 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.

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Last modified: February 21, 2007