Overdetermined partial resolvent kernels for finite networks
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- 作者：C. Araú ; z ; A. Carmona ; angeles.carmona@upc.edu" class="auth_mail" title="E-mail the corresponding author ; A.M. Encinas
- 关键词：Overdetermined partial boundary value problems ; Dirichlet-to-Neumann map ; Inverse problem ; Resolvent Kernels
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2016
- 出版时间：1 March 2016
- 年：2016
- 卷：435
- 期：1
- 页码：96-111
- 全文大小：381 K
文摘
In [2], a study of the existence and uniqueness of solution of partial overdetermined boundary value problems for finite networks was performed. These problems involve Schrödinger operators and the novel feature is that no data are prescribed on part of the boundary, whereas both the values of the function and of its normal derivative are given on another part of the boundary. In the present work, we study the resolvent kernels associated with overdetermined partial boundary value problems on finite network and we express them in terms of the well-known Green operator and the Dirichlet-to-Robin map. Moreover, we analyze their main properties and we compute them in the case of a generalized cylinder. The obtained expression involve polynomials that can be seen as a generalization of Chebyshev polynomials, and indeed when the conductances along axes are constant the expressions for the overdetermined partial resolvent kernels are given in terms of second kind Chebyshev polynomials.