Sobolev空间在数学III：应用在数学物理中

English | PDF | 2009 | 360 Pages | ISBN : 038785651X | 4.3 MB

The mathematical works of S.L.Sobolev were strongly motivated by particular problems coming from applications. In his celebrated book Applications of Functional Analysis in Mathematical Physics, 1950 and other works, S.Sobolev introduced general methods that turned out to be very influential in the study of mathematical physics in the second half of the XXth century. This volume, dedicated to the centenary of S.L. Sobolev, presents the latest results on some important problems of mathematical physics describing, in particular, phenomena of superconductivity with random fluctuations, wave propagation, perforated domains and bodies with defects of different types, spectral asymptotics for Dirac energy, Lam\'e system with residual stress, optimal control problems for partial differential equations and inverse problems admitting numerous interpretations. Methods of modern functional analysis are essentially used in the investigation of these problems.

S.L. 柯尔莫 logarithm 卡洛夫的数学著作深受应用领域特定问题的启发。他在《泛函分析在数学物理中的应用》（1950 年）和其他作品中引入了一般方法，这些方法对 20 世纪后半叶的数理物理学研究产生了深远的影响。该纪念专著《S.L. 柯尔莫 logarithm 卡洛夫诞辰百年纪念》涵盖了当前最重要的数理物理问题的研究成果，这些问题包括描述例如具有随机波动现象的超导性、波传播、有缺陷域和不同类型的体、狄拉克能量的谱渐近特性、带有残余应力的拉梅系统的解析及最优控制问题对于偏微分方程的优化控制问题以及多种解释的反问题。现代泛函分析的基本方法在这些问题的研究中得到了广泛的应用。

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