Abstract
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. The author obtains a priori bounds for solutions in the Zygmund space, which is wider than the Lipschitz space C 1,1 but narrower than the Holder space C 1, α, 0 < α < 1. Also, the first and second boundary-value problems are considered for the heat equation with similar conditions. It is shown that the solutions belong to the corresponding Zygmund space.
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