Continuous and variable branching asymptotics

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• 作者：M. Hedayat Mahmoudi (1)
  B.-W. Schulze (1)
  L. Tepoyan (2)
  
  1. Institute of Mathematics ; University of Potsdam ; Am Neuen Palais 10 ; 14469 ; Potsdam ; Germany
  2. Department of Mathematics and Mechanics ; Yerevan State University ; A. Manoogian str. 1 ; 0025 ; Yerevan ; Armenia
  
• 关键词：Asymptotics of solutions ; Weighted edge spaces ; Edge symbols ; Primary 35S35 ; Secondary 35J70
• 刊名：Journal of Pseudo-Differential Operators and Applications
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：6
• 期：1
• 页码：69-112
• 全文大小：433 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：None Assigned
• 出版者：Birkh盲user Basel
• ISSN：1662-999X

文摘

The regularity of solutions to elliptic equations on a manifold with singularities, say, an edge, can be formulated in terms of asymptotics in the distance variable \(r>0\) to the singularity. In simplest form such asymptotics turn to a meromorphic behaviour under applying the Mellin transform on the half-axis. Poles, multiplicity, and Laurent coefficients form a system of asymptotic data which depend on the specific operator. Moreover, these data may depend on the variable \(y\) along the edge. We then have \(y\) -dependent families of meromorphic functions with variable poles, jumping multiplicities and a discontinuous dependence of Laurent coefficients on \(y.\) We study here basic phenomena connected with such variable branching asymptotics, formulated in terms of variable continuous asymptotics with a \(y\) -wise discrete behaviour.