Elliptic Partial Differential Equations
Elliptic Partial Differential Equations
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DOI：
10.1007/978-3-0346-0537-3
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发表时间：
2011-12
期刊：
影响因子：
--
通讯作者：
V. Volpert
中科院分区：
文献类型：
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作者：
V. Volpert
椭圆型偏微分方程的理论在过去的两个世纪里经历了一个重要的发展。与静电学、热扩散和质量扩散、流体力学和许多其他应用一起，它已成为数学中最丰富的领域之一。这本专著承担一般椭圆算子理论的系统介绍。作者讨论了先验估计，正常的可解性，Fredholm性质，指数的椭圆算子，运营商的参数，和非线性Fredholm运营商。特别注意的是椭圆问题的无界域尚未得到充分的处理，在文献中，需要一些特殊的方法。这本书还包含了非Fredholm算子和离散算子的分析以及广泛的历史和书目评论。选定的主题和作者的话语水平将使这本书成为研究人员和研究生在偏微分方程和应用的广泛领域工作的最有用的资源。
The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments. The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.