Geodesic
On a partial differential equation in 4-dimensional Euclidean space
Lobachevskii journal of mathematics, Tome 18 (2005), pp. 151-175 
E. A. Utkina. On a partial differential equation in 4-dimensional Euclidean space. Lobachevskii journal of mathematics, Tome 18 (2005), pp. 151-175. http://geodesic.mathdoc.fr/item/LJM_2005_18_a8/
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     author = {E. A. Utkina},
     title = {On a partial differential equation in 4-dimensional {Euclidean} space},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2005_18_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The objective of this article is to construct in a hyper-rectangular region of the 4-dimensional Euclidean space a solution of the Goursat problem for the following equation: $$ L(u)=\sum_{i_1=0}^{m_1}\sum_{i_2=0}^{m_2}\sum_{i_3=0}^{m_3}\sum_{i_4=0}^{m_4}a_{i_1i_2i_3i_4}(x_1,x_2,x_3,x_4)\frac{\partial^{i_1+i_2+i_3+i_4}u}{\partial x_1^{i_1}\partial x_2^{i_2}\partial x_3^{i_3}\partial x_4^{i_4}}=F(x_1,x_2,x_3,x_4). $$

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