Harmonic Maps Between Surfaces: With a Special Chapter on Conformal Mappings (Lecture Notes in Mathematics)

Science & Math

Jürgen Jost

Mathematics

Springer, Verlag

This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups. This second edition features a new chapter on reaction-diffusion equations and systems.

Partial Differential Equations (Graduate Texts in Mathematics)

Springer

Choices in Palliative Care: Issues in Health Care Delivery

Introduction to advanced analysis at the beginNING graduated level that blends a modern presentation with concrete examples and applications, in particular, in the areas of calculus of variations and partial differential equations. Paper. DLC: mathematical analysis.

Postmodern Analysis (Universitext)

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. 
The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. ... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews
"...the material ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section ‘Perspectives’, written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH

Riemannian Geometry and Geometric Analysis (Universitext)

Springer Nature

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Books by Jürgen Jost