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Titlebook: Variational Methods in Mathematical Physics; A Unified Approach Philippe Blanchard,Erwin Brüning Textbook 1992 Springer-Verlag Berlin Heide

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书目名称Variational Methods in Mathematical Physics
副标题A Unified Approach
编辑Philippe Blanchard,Erwin Brüning
视频video
丛书名称Theoretical and Mathematical Physics
图书封面Titlebook: Variational Methods in Mathematical Physics; A Unified Approach Philippe Blanchard,Erwin Brüning Textbook 1992 Springer-Verlag Berlin Heide
描述The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal­ culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are
出版日期Textbook 1992
关键词Eigenvalue; Funktionalanalyse; Mathematische Physik; Mechanik; Quantenmechanik; compactness; functional an
版次1
doihttps://doi.org/10.1007/978-3-642-82698-6
isbn_softcover978-3-642-82700-6
isbn_ebook978-3-642-82698-6Series ISSN 1864-5879 Series E-ISSN 1864-5887
issn_series 1864-5879
copyrightSpringer-Verlag Berlin Heidelberg 1992
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Classical Variational Problems,ical terms, this means that the functional . has the form . where we have a certain function. and a compact interval .= [.] or, alternatively, an equivalent generalisation to functions . of several variables and to functions . with values in ℝ., .>1.
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Thomas-Fermi Theory,ariations. Questions of validity and physical interpretation are discussed by Thirring [10.1] and Lieb and Simon [10.2] and in references quoted therein. Justification for statements which we do not prove below can be found in [10.1, 3].
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Semilinear Elliptic Differential Equations. Some Recent Results on Global Solutions,All the results on concrete boundary and eigenvalue problems presented in Chaps. 6–8 use in an essential way at least one of the following two assumptions:
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Theoretical and Mathematical Physicshttp://image.papertrans.cn/v/image/980595.jpg
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