Partial Differential Equations III

1. Front Matter

   Pages i-xxii

   PDF

2. Function Space and Operator Theory for Nonlinear Analysis

   • Michael E. Taylor

   Pages 1-104

3. Nonlinear Elliptic Equations

   • Michael E. Taylor

   Pages 105-311

4. Nonlinear Parabolic Equations

   • Michael E. Taylor

   Pages 313-411

5. Nonlinear Hyperbolic Equations

   • Michael E. Taylor

   Pages 413-529

6. Euler and Navier—Stokes Equations for Incompressible Fluids

   • Michael E. Taylor

   Pages 531-614

7. Einstein’s Equations

   • Michael E. Taylor

   Pages 615-709

8. Back Matter

   Pages 711-715

   PDF

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

• Einstein's equations
• Navier-Stokes equations
• Nonlinear elliptic equations
• Nonlinear hyperbolic equations
• partial differential equations

From the reviews:

“These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”(SIAM Review, June 1998)

From the reviews of the second edition:

“This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. … Graduate students … will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. … an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics.” (Christian Constanda, The Mathematical Association of America, July, 2011)

• Department of Mathematics, University of North Carolina, Chapel Hill, USA

  Michael E. Taylor

Michael E. Taylor is a Professor at University of North Carolina in the Department of Mathematics.