Elliptic & Parabolic EquationsThis book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them. |
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Índice
Preliminary Knowledge | 1 |
L2 Theory of Linear Elliptic Equations | 39 |
L2 Theory of Linear Parabolic Equations | 71 |
De Giorgi Iteration and Moser Iteration | 105 |
Harnacks Inequalities | 131 |
Schauders Estimates for Linear Elliptic Equations | 159 |
Schauders Estimates for Linear Parabolic Equations | 197 |
Existence of Classical Solutions for Linear Equations | 233 |
Strong Solutions | 255 |
Fixed Point Method | 277 |
Topological Degree Method | 313 |
Monotone Method | 323 |
Degenerate Equations | 355 |
Bibliography | 403 |
Otras ediciones - Ver todo
Elliptic & Parabolic Equations Zhuoqun Wu,Jingxue Yin,Chunpeng Wang No hay ninguna vista previa disponible - 2006 |
Términos y frases comunes
admits a unique Assume Banach space boundary value condition bounded domain bounded linear BR(x C(QT Cauchy's inequality Chapter choose classical solutions converges Corollary cut-off function defined definition of weak Denote derive Dirichlet problem dpQT Dw\2dxdt dxdt elliptic equations embedding theorem establish exists a constant G QT Harnack's inequality heat equation Hence Holder's estimate Hq(Q implies initial-boundary value problem integrating interior estimate JJq+ JJQp JJQr JJQt JJQt Jn Jn Laplace's equation Let u G Lipschitz continuous LP estimates LP norm mapping maximum principle nondecreasing ordered supersolution parabolic equations Poincare's inequality Poisson's equation positive constant depending Prom proof of Theorem Proposition quasilinear quasimonotone Remark satisfies Schauder's estimates sequence Sobolev spaces solution of equation solution of problem space strong solution supersolution and subsolution supu u2dx u2dxdt unique solution weak derivatives weak solution weak subsolution x,t)eQT
Información bibliográfica
| Título | Elliptic & Parabolic Equations Elliptic & Parabolic Equations, Chunpeng Wang |
| Autores | Zhuoqun Wu, Jingxue Yin, Chunpeng Wang |
| Editor | World Scientific, 2006 |
| ISBN | 9812700250, 9789812700254 |
| N.º de páginas | 408 páginas |
| Exportar cita | BiBTeX EndNote RefMan |