Geodesic
On a non-standard conjugation problem for elliptic equations
Matematičeskie zametki SVFU, Tome 23 (2016) no. 3, pp. 70-80 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the regular solvability of the conjugation problem for elliptic equations with non-standard boundary conditions and sewing conditions on the plane $x = 0$. Let $Q$ be a parallelepiped. On the bottom of $Q$ we give a boundary condition for $u(x, t, a)$ in the part where $x>0$ and for $u_t(x, t, a)$ in the part where $x<0$. On the plane $x=0$ these conditions “intertwist”, so on the top of $Q$ we give a boundary condition for $u(x, t, a)$ in the part where $x<0$ and for $u_t(x, t, a)$ in the part where $x > 0$. Combining the regularization method and natural parameter continuation, we prove the uniqueness and existence theorems for regular solutions of this non-standard conjugation problem.
Mots-clés : conjugation problem, elliptic equation
Keywords: regular solution, sewing condition, discontinuous boundary conditions. 
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     author = {A. I. Kozhanov and S. V. Potapova},
     title = {On a non-standard conjugation problem for elliptic equations},
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     url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_3_a4/}
}
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A. I. Kozhanov; S. V. Potapova. On a non-standard conjugation problem for elliptic equations. Matematičeskie zametki SVFU, Tome 23 (2016) no. 3, pp. 70-80. http://geodesic.mathdoc.fr/item/SVFU_2016_23_3_a4/

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