Partial Differential Equations, 3 Vols., Geb. Vol.3 Nonlinear Equations (Applied Mathematical Sciences Vol.117)

Taylor, Michael E.

springer（2006/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 610 p.
• 言語 ENG
• 商品コード 9780387946528

Full Description

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis.

Contents

13) Function space and operator theory for nonlinear analysis; 14) Nonlinear elliptic equations; 15) Nonlinear parabolic equations; 16) Nonlinear hyperbolic equations; 17) Euler and Navier-Stokes equations for incompressible fluids; 18) Einstein's equations