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Titlebook: Boundary Integral Equations; George C. Hsiao,Wolfgang L. Wendland Book 2021Latest edition Springer Nature Switzerland AG 2021 Fredholm alt

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发表于 2025-3-21 19:28:46 | 显示全部楼层 |阅读模式
期刊全称Boundary Integral Equations
影响因子2023George C. Hsiao,Wolfgang L. Wendland
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发行地址This book contains two parts: The first six chapters present the modern mathematical theory of boundary integral equations with applications on fundamental problems in continuum mechanics and electrom
学科分类Applied Mathematical Sciences
图书封面Titlebook: Boundary Integral Equations;  George C. Hsiao,Wolfgang L. Wendland Book 2021Latest edition Springer Nature Switzerland AG 2021 Fredholm alt
影响因子.This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics..The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding
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Sobolev Spaces,e Sobolev spaces provide a very natural setting for variational problems. This chapter contains a brief summary of the basic definitions and results of the .–theory of Sobolev spaces which will suffice for our purposes.
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Variational Formulations,differential equations. We collect some basic theorems in functional analysis which are needed for this purpose. In particular, Green‘s theorems and the Lax–Milgram theorem are fundamental tools for the solvability of boundary integral equations as well as for elliptic partial differential equations
发表于 2025-3-22 10:47:13 | 显示全部楼层
Pseudodifferential and Boundary Integral Operators,ral operators including those presented in the previous chapters belong to the special class of classical pseudodifferential operators on compact manifolds. We are particularly interested in strongly elliptic systems of pseudodifferential operators providing Gårding‘s inequality, see Theorem 9.1.4.
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Boundary Integral Equations on Curves in , ,In this chapter we present the two–dimensional theory of classical pseudodifferential and boundary integral operators based on Fourier analysis. In general, the representations of boundary potentials are based on the local charts and local coordinates (3.3.3)–(3.3.5).
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Remarks on Pseudodifferential Operators Related to the Time Harmonic Maxwell Equations,solutions of elliptic differential operators and all integral operators with pseudohomogeneous kernel expansions. The linear pseudodifferential operators can be characterized by generalized Fourier multipliers, known as .. The development of the theory of pseudodifferential operators has made it pos
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Low Threshold Organic Semiconductor Lasersachinery. This includes the basic definitions and properties of classical function spaces and distributions, the Fourier transform and the definition of Hadamard‘s finite part integrals which, in fact, represent the natural regularization of homogeneous distributions and of the hypersingular boundary integral operators.
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