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On the solvability of the first nonlocal boundary value problem for an elliptic equation

On the solvability of the first nonlocal boundary value problem for an elliptic equation We consider problems of the existence, uniqueness, and sign-definiteness of the classical solutions of the problem $$ (Lu)(x) = f(x)(x \in D),u(x) - \beta (x)u(\sigma x) = \psi (x)(x \in S), $$ where L is a linear second-order operator elliptic in the closure of a domain D ⊂ R n and σ is a single-valued continuous mapping of S ≡ ∂D into $$ \bar D $$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the solvability of the first nonlocal boundary value problem for an elliptic equation

Ratyni, A.
Differential Equations , Volume 45 (6) – Jul 19, 2009
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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Pleiades Publishing, Ltd.
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S001226610906007X
Publisher site
See Article on Publisher Site

Abstract

We consider problems of the existence, uniqueness, and sign-definiteness of the classical solutions of the problem $$ (Lu)(x) = f(x)(x \in D),u(x) - \beta (x)u(\sigma x) = \psi (x)(x \in S), $$ where L is a linear second-order operator elliptic in the closure of a domain D ⊂ R n and σ is a single-valued continuous mapping of S ≡ ∂D into $$ \bar D $$ .

Journal

Differential Equations – Springer Journals

Published: Jul 19, 2009

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