On variational formulations of inner boundary value problems for infinite systems of elliptic equations of special kind

Author Yu. A. Muzychuk, R. S. Chapko
yuriy.muzychuk@gmail.com, roman.chapko@gmail.com
Ivan Franko National University of Lviv

Abstract We consider boundary value problems for infinite triangular systems of elliptic equations with variable coefficients in 3d Lipschitz domains. Variational formulations of Dirichlet, Neumann and Robin problems are received and their well posedness in corresponding Sobolev spaces is established. With the help of introduced q-convolution the integral representations of generalized solutions of formulated problems in the case of constant coefficients are built. We investigate the properties of integral operators and well posedness of received systems of boundary integral equations.
Keywords elliptic equation; infinite system; Sobolev spaces; Lipschitz boundary; variational formulation; generalized solution; Green formulae; layer potential
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Pages 12-34
Volume 38
Issue 1
Year 2012
Journal Matematychni Studii
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