《變分法第四版》是2012年3月1日世界圖書出版社出版的圖書，作者是 Michael Struwe 。
基本介紹
- 中文名：變分法第四版
- 作者：Michael Struwe
- ISBN：9787510042874
- 定價：34.20元
- 出版社：世界圖書出版社
- 出版時間：2012年3月1日
內容簡介,圖書目錄,
內容簡介
《變分法（第4版）》是《變分法》第四版，主要講述在非線性偏微分方程和哈密頓系統中的套用，繼第一版出版十八年再次全新呈現。整《變分法（第4版）》都做了大量的修改，僅500多條參考書目就將其價值大大提升。第四版中主要講述變分微積分，增加了該領域的新進展。這也是一部變分法學習的教程，特別講述了yamabe流的收斂和脹開現象以及新研究發現的調和映射和曲面中熱流的向後小泡形成。
圖書目錄
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
