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S. Agmon (1965)
Lectures on Elliptic Boundary Value Problems
E. Stein (1971)
Singular Integrals and Di?erentiability Properties of Functions
Di erential Equations, Vol. 37, No. 12, 2001, pp. 1699{1710. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 12, 2001, pp. 1618{1628. Original Russian Text Copyright c 2001 by Gasymov, Aslanov. PARTIAL DIFFERENTIAL EQUATIONS Existence and the Asymptotic Behavior of Generalized Solutions of the Neumann Problem for Second-Order Elliptic Equations in Unbounded Layer Domains M. G. Gasymov and G. I. Aslanov Azerbaijan Technical University, Baku, Azerbaijan Received May 18, 2001 Boundary value problems for elliptic equations in unbounded domains were considered in many papers [1{5]. The case of an in nite cylinder (n = 1) and a problem periodic in part of the variables for a second-order elliptic equation are best studied [6]. The existence of solutions was not usually dealt with in previous works, and only the properties of apriori known solutions were analyzed. It was assumed in [5, 6] that such a solution has a nite Dirichlet integral. The Laplace equation on Riemannian manifolds of structure more general than that of a layer was considered in [7]. The present paper continues and develops the studies initiated in [8, 9]. Here we analyze the existence and analytic behavior of a generalized solution of the Neumann problem for a
Differential Equations – Springer Journals
Published: Oct 9, 2004
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