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P. Krutitskii (2001)
The jump problem for the Laplace equationAppl. Math. Lett., 14
Differential Equations, Vol. 39, No. 9, 2003, pp. 1225–1236. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 9, 2003, pp. 1165–1175. Original Russian Text Copyright c 2003 by Krutitskii, Sgibnev. PARTIAL DIFFERENTIAL EQUATIONS Singularities of the Solution Gradient in the Generalized Jump Problem for the Laplace Equation Outside a Cut on the Plane P. A. Krutitskii and A. I. Sgibnev Moscow State University, Moscow, Russia Received March 3, 2003 INTRODUCTION Boundary value problems outside open curves on the plane have numerous applications in physics and mechanics, since the cuts model cracks in rigid bodies, wings and shields in liquids and gases, electrodes in semiconductors, and so on. The Dirichlet and Neumann problems for the Helmholtz equation outside cuts on the plane were considered in [1, 2]. Mixed problems for the Helmholtz equa- tion were considered in [3, 4] for the case in which the Dirichlet condition is posed on one set of cuts and the Neumann condition on the other. The work [5] dealt with the mixed problem for the Laplace equation in which the Dirichlet condition is posed on one part of cuts and an oblique derivative condition on the other. Such problems arise in semiconductor physics. Another mixed
Differential Equations – Springer Journals
Published: Oct 5, 2004
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