Geodesic
Dirichlet and Neumann problems for Laplace and heat equations in domains with right angles
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 75-82 
A. N. Konenkov. Dirichlet and Neumann problems for Laplace and heat equations in domains with right angles. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 75-82. http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a6/
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     author = {A. N. Konenkov},
     title = {Dirichlet and {Neumann} problems for {Laplace} and heat equations in domains with right angles},
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     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $C^{1,1}$ but narrower that the Hölder space $C^{1,\alpha}$, $0\alpha1$. 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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