Iii: Nonlinear E... | Partial Differential Equations

The "story" of the book is structured around the three fundamental types of partial differential equations, now viewed through a nonlinear lens.

and deeper connections in complex geometry. Go to product viewer dialog for this item. Partial Differential Equations III: Nonlinear Equations Partial Differential Equations III: Nonlinear E...

Sobolev, Hölder, Hardy, and Morrey spaces to measure the regularity and "smoothness" of solutions. The "story" of the book is structured around

: The narrative peaks with General Relativity , where the geometry of space-time itself is treated as a nonlinear PDE system. New in the Third Edition (2023) : This covers "diffusion" processes where things spread

and probabilistic interpretations of these equations.

: This covers "diffusion" processes where things spread out over time. Key topics include semilinear equations and their applications to Harmonic Maps and reaction-diffusion systems, which model everything from chemical reactions to biological patterns.

: This section explores the "static" side of math and physics. It dives into Differential Geometry , studying minimal surfaces (like the shape of a soap film) and the Isometric Imbedding of Riemannian Manifolds .