变分法（第4版） [Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamilton 下载 mobi epub pdf 电子书 2024

☆☆☆☆☆
简体网页||繁体网页



点击这里下载

类似图书 点击查看全场最低价

---

内容简介

　　 《变分法（第4版）》是《变分法》第四版，主要讲述在非线性偏微分方程和哈密顿系统中的应用，继第一版出版十八年再次全新呈现。整《变分法（第4版）》都做了大量的修改，仅500多条参考书目就将其价值大大提升。第四版中主要讲述变分微积分，增加了该领域的新进展。这也是一部变分法学习的教程，特别讲述了yamabe流的收敛和胀开现象以及新研究发现的调和映射和曲面中热流的向后小泡形成。

内页插图

目录

Chapter I.the direct methods in the calculus of variations
1.lower semi-continuity
degenerate elliptic equations
-minimal partitioning hypersurfaces
-minimal hypersurfaces in riemannian manifolds
-a general lower semi-continuity result
2.constraints
semilinear elliptic boundary value problems
-perron's method in a variational guise
-the classical plateau problem
3.compensated compactness
applications in elasticity
-convergence results for nonlinear elliptic equations
-hardy space methods
4.the concentration-compactness principle
existence of extremal functions for sobolev embeddings
5.ekeland's variational principle
existence of minimizers for quasi-convex functionals
6.duality
hamiltonian systems
-periodic solutions of nonlinear wave equations
7.minimization problems depending on parameters
harmonic maps with singularities

Chapter Ⅱ.minimax methods
1.the finite dimensional case
2.the palais-smale condition
3.a general deformation lemma
pseudo-gradient flows on banach spaces
-pseudo-gradient flows on manifolds
4.the minimax principle
closed geodesics on spheres
5.index theory
krasnoselskii genus
-minimax principles for even functional
-applications to semilinear elliptic problems
-general index theories
-ljusternik-schnirelman category
-a geometrical si-index
-multiple periodic orbits of hamiltonian systems
6.the mountain pass lemma and its variants
applications to semilinear elliptic boundary value problems
-the symmetric mountain pass lemma
-application to semilinear equa- tions with symmetry
7.perturbation theory
applications to semilinear elliptic equations
8.linking
applications to semilinear elliptic equations
-applications to hamil- tonian systems
9.parameter dependence
10.critical points of mountain pass type
multiple solutions of coercive elliptic problems
11.non-differentiable fhnctionals
12.ljnsternik-schnirelman theory on convex sets
applications to semilinear elliptic boundary value problems

Chapter Ⅲ.Limit cases of the palais-smale condition
1.pohozaev's non-existence result
2.the brezis-nirenberg result
constrained minimization
-the unconstrained case： local compact- ness
-multiple solutions
3.the effect of topology
a global compactness result, 184 -positive solutions on annular-shaped regions, 190
4.the yamabe problem
the variational approach
-the locally conformally flat case
-the yamabe flow
-the proof of theorem4.9 （following ye [1]）
-convergence of the yamabe flow in the general case
-the compact case ucc
-bubbling： the casu
5.the dirichlet problem for the equation of constant mean curvature
small solutions
-the volume functional
- wente's uniqueness result
-local compactness
-large solutions
6.harmonic maps of riemannian surfaces
the euler-lagrange equations for harmonic maps
-bochner identity
-the homotopy problem and its functional analytic setting
-existence and non-existence results
-the heat flow for harmonic maps
-the global existence result
-the proof of theorem 6.6
-finite-time blow-up
-reverse bubbling and nonuniqueness

appendix a
sobolev spaces
-hslder spaces
-imbedding theorems
-density theorem
-trace and extension theorems
-poincar4 inequality
appendix b
schauder estimates
-lp-theory
-weak solutions
-areg-ularityresult
-maximum principle
-weak maximum principle
-application
appendix c
frechet differentiability
-natural growth conditions
references
index

精彩书摘

Almost twenty years after conception of the first edition， it was a challenge to prepare an updated version of this text on the Calculus of Variations. The field has truely advanced dramatically since that time， to an extent that I find it impossible to give a comprehensive account of all the many important developments that have occurred since the last edition appeared. Fortunately， an excellent overview of the most significant results， with a focus on functional analytic and Morse theoretical aspects of the Calculus of Variations， can be found in the recent survey paper by Ekeland-Ghoussoub [1]. I therefore haveonly added new material directly related to the themes originally covered.
Even with this restriction， a selection had to be made. In view of the fact that flow methods are emerging as the natural tool for studying variational problems in the field of Geometric Analysis， an emphasis was placed on advances in this domain. In particular， the present edition includes the proof for the convergence of the Yamabe flow on an arbitrary closed manifold of dimension 3 m 5 for initial data allowing at most single-point blow-up.Moreover， we give a detailed treatment of the phenomenon of blow-up and discuss the newly discovered results for backward bubbling in the heat flow for harmonic maps of surfaces.
Aside from these more significant additions， a number of smaller changes have been made throughout the text， thereby taking care not to spoil the freshness of the original presentation. References have been updated， whenever possible， and several mistakes that had survived the past revisions have now been eliminated. I would like to thank Silvia Cingolani， Irene Fouseca， Emmanuel Hebey， and Maximilian Schultz for helpful comments in this regard. Moreover，I am indebted to Gilles Angelsberg， Ruben Jakob， Reto Miiller， and Melanie Rupfiin， for carefully proof-reading the new material.
……

前言/序言

变分法（第4版） [Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamilton 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

好好好

评分☆☆☆☆☆

对于要学习变分法的同学，这本书是很经典的书，不过比较难读，有深度

评分☆☆☆☆☆

很好，趁活动买的。

评分☆☆☆☆☆

非常好的经典书籍 一定要仔细看。

评分☆☆☆☆☆

Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems 4th ed

评分☆☆☆☆☆

看着压力山大，希望自己能看明白··

评分☆☆☆☆☆

变分法（calculus of variations），是处理函数的函数的数学领域，和处理数的函数的普通微积分相对。譬如，这样的泛函可以通过未知函数的积分和它的导数来构造。变分法最终寻求的是极值函数：它们使得泛函取得极大或极小值。有些曲线上的经典问题采用这种形式表达：一个例子是最速降线，在重力作用下一个粒子沿着该路径可以在最短时间从点A到达不直接在它底下的一点B。在所有从A到B的曲线中必须极小化代表下降时间的表达式。

评分☆☆☆☆☆

一般啦一般啦一般啦一般啦

评分☆☆☆☆☆

非常不错，已经多次购买了！

类似图书 点击查看全场最低价