出 版 社：世界圖書出版公司
出版時間：2011-6-1
版 次：1
頁 數：388
印刷時間：2011-6-1
開 本：24開
紙 張：膠版紙
印 次：1
I S B N：9787510035166
包 裝：平裝
內容簡介
《偏微分方程(第2卷)》是一部兩卷集的偏微分方程教材。多變數橢圓，拋物和雙曲方程是研究的主要對象，解決了pde和多變數方法之間的關係。本書是第二卷主要講述了banach空間運算元方程的可解性，hilbert空間線性運算元和譜理論；線性橢圓微分方程的schauder理論；微分方程弱解；非線性偏微分方程；非線性橢圓系統和微分幾何套用。書中各章的獨立性較強，有一定偏微分方程基本知識的讀者可以獨立閱讀各章。目次：banach空間中的運算元；hilbert空間線性運算元；線性橢圓微分方程；非線性偏微分方程；非線性橢圓系統。
讀者對象：數學專業的本科生，研究生和相關的科研人員。
目錄
vii operators in banach spaces
1 fixed point theorems
2 the leray-schauder degree of mapping
3 fundamental properties for the degree of mapping
4 linear operators in banach spaces
5 some historical notices to the chapters iii and vii
viii linear operators in hilbert spaces
1 various eigenvalue problems
2 singular integral equations
3 the abstract hilbert space
4 bounded linear operators in hilbert spaces
5 unitary operators
6 completely continuous operators in hilbert spaces
7 spectral theory for completely continuous hermitian operators
8 the sturm-liouville eigenvalue problem
9 weyl's eigenvalue problem for the Laplace operator
9 some historical notices to chapter viii
ix linear elliptic differential equations
1 the differential equation △φ+p(x, y)φx+q(x, y)φy=r(x, y)
2 the schwarzian integral formula
3 the riemann-hilbert boundary value problem
4 potential-theoretic estimates.
5 schauder's continuity method
6 existence and regularity theorems
7 the schauder estimates
8 some historical notices to chapter ix
x weak solutions of elliptic differential equations
1 sobolev spaces
2 embedding and compactness
3 existence of weak solutions
4 boundedness of weak solutions
5 hslder continuity of weak solutions
6 weak potential-theoretic estimates
7 boundary behavior of weak solutions
8 equations in divergence form
9 green's function for elliptic operators
10 spectral theory of the laplace-beltrami operator
11 some historical notices to chapter x
xi nonlinear partial differential equations
1 the fundamental forms and curvatures of a surface
2 two-dimensional parametric integrals
3 quasilinear hyperbolic differential equations and systems of second order (characteristic parameters)
4 cauchy's initial value problem for quasilinear hyperbolic differential equations and systems of second order
5 riemann's integration method
6 bernstein's analyticity theorem
7 some historical notices to chapter xi
xii nonlinear elliptic systems
1 maximum principles for the h-surface system
2 gradient estimates for nonlinear elliptic systems
3 global estimates for nonlinear systems
4 the dirichlet problem for nonlinear elliptic systems
5 distortion estimates for plane elliptic systems
6 a curvature estimate for minimal surfaces
7 global estimates for conformal mappings with respect to riemannian metrics
8 introduction of conformal parameters into a riemannian metric
9 the uniformization method for quasilinear elliptic differential equations and the dirichlet problem
10 an outlook on plateau's problem
11 some historical notices to chapter xii
