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Titlebook: Crack Theory and Edge Singularities; David Kapanadze,B.-Wolfgang Schulze Book 2003 Springer Science+Business Media Dordrecht 2003 Boundary

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發(fā)表于 2025-3-21 19:35:52 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Crack Theory and Edge Singularities
編輯David Kapanadze,B.-Wolfgang Schulze
視頻videohttp://file.papertrans.cn/240/239235/239235.mp4
概述Systematically develops for the first time an approach in terms of algebras of (pseudo-differential) boundary value problems
叢書名稱Mathematics and Its Applications
圖書封面Titlebook: Crack Theory and Edge Singularities;  David Kapanadze,B.-Wolfgang Schulze Book 2003 Springer Science+Business Media Dordrecht 2003 Boundary
描述Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in corresponding models are then sin- gular or degenerate in a typical way. The necessary structures for constructing solutions belong to a particularly beautiful and ambitious part of the analysis. Cracks in a medium are described by hypersurfaces with a boundary. Config- urations of that kind belong to the category of spaces (manifolds) with geometric singularities, here with edges. In recent years the analysis on such (in general, stratified) spaces has become a mathematical structure theory with many deep relations with geometry, topology, and mathematical physics. Key words in this connection are operator algebras, index theory, quantisation, and asymptotic analysis. Motivated by Lame‘s system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys- tems in general. We construct parametric
出版日期Book 2003
關(guān)鍵詞Boundary value problem; analytic function; differential calculus; differential operator; manifold; partia
版次1
doihttps://doi.org/10.1007/978-94-017-0323-9
isbn_softcover978-90-481-6384-7
isbn_ebook978-94-017-0323-9
copyrightSpringer Science+Business Media Dordrecht 2003
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沙發(fā)
發(fā)表于 2025-3-21 21:51:43 | 只看該作者
Operators on manifolds with conical singularities,are assumed to have the transmission property at the smooth part of the boundary. For crack problems below we will apply the calculus to an infinite two-dimensional cone with boundary. The cone algebra in this case plays the role of a range of operator-valued symbols for a corresponding crack operat
板凳
發(fā)表于 2025-3-22 03:40:45 | 只看該作者
地板
發(fā)表于 2025-3-22 08:19:23 | 只看該作者
Boundary value problems on manifolds with edges,blems on . with extra trace and potential conditions on the edge and (edge-degenerate) pseudo-differential operators on ., together with trace and potential conditions and (standard) pseudo-differential operators on .. The calculus consists of a 3 × 3 block matrix algebra with a three-component symb
5#
發(fā)表于 2025-3-22 09:48:22 | 只看該作者
Book 2003on, and asymptotic analysis. Motivated by Lame‘s system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys- tems in general. We construct parametric
6#
發(fā)表于 2025-3-22 15:59:44 | 只看該作者
ic analysis. Motivated by Lame‘s system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys- tems in general. We construct parametric978-90-481-6384-7978-94-017-0323-9
7#
發(fā)表于 2025-3-22 19:42:08 | 只看該作者
https://doi.org/10.1007/978-94-017-0323-9Boundary value problem; analytic function; differential calculus; differential operator; manifold; partia
8#
發(fā)表于 2025-3-22 21:53:03 | 只看該作者
978-90-481-6384-7Springer Science+Business Media Dordrecht 2003
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發(fā)表于 2025-3-23 05:04:20 | 只看該作者
10#
發(fā)表于 2025-3-23 05:42:55 | 只看該作者
Operators on manifolds with exits to infinity,with a special control for . → .. Wedge operators are pseudo-differential operators with cone operator-valued symbols. They are connected with groups of isomorphisms in weighted Sobolev spaces on the infinite cone, induced by homotheties in the axial variable, and . → . is regarded as a non-compact exit of the cone to infinity.
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