Elliptic problems on networks with constrictions

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• 作者：Jacob Rubinstein ; Peter Sternberg and Gershon Wolansky
• 关键词：Differential equations on graphs ; Ginzburg ; Landau theory
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2006
• 出版时间：August 2006
• 年：2006
• 卷：26
• 期：4
• 页码：459-487
• 全文大小：476 KB

文摘

We investigate the asymptotic behavior of minimizers to sequences of elliptic variational problems posed on thin three-dimensional domains. These domains arise as thin neighborhoods of artibrary graphs that contain severe constrictions near the graph nodes. We characterize an appropriate limit of minimizers as a function of one variable defined on the graph that necessarily minimizes a one-dimensional variational problem. The most salient feature of these limits of minimizers is the emergence of jump discontinuities across the graph nodes. While the approach can handle quite general elliptic problems, we pay particular attention to an application to generalized Josephson junctions within the Ginzburg-Landau theory of superconductivity.