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The Monge-Ampere Equation (Hardcover, 2nd ed. 2016)
Loot Price: R6,157
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The Monge-Ampere Equation (Hardcover, 2nd ed. 2016)
Series: Progress in Nonlinear Differential Equations and Their Applications, 89
Expected to ship within 10 - 15 working days
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Now in its second edition, this monograph explores the Monge-Ampere
equation and the latest advances in its study and applications. It
provides an essentially self-contained systematic exposition of the
theory of weak solutions, including regularity results by L. A.
Caffarelli. The geometric aspects of this theory are stressed using
techniques from harmonic analysis, such as covering lemmas and set
decompositions. An effort is made to present complete proofs of all
theorems, and examples and exercises are offered to further
illustrate important concepts. Some of the topics considered
include generalized solutions, non-divergence equations, cross
sections, and convex solutions. New to this edition is a chapter on
the linearized Monge-Ampere equation and a chapter on interior
Hoelder estimates for second derivatives. Bibliographic notes,
updated and expanded from the first edition, are included at the
end of every chapter for further reading on Monge-Ampere-type
equations and their diverse applications in the areas of
differential geometry, the calculus of variations, optimization
problems, optimal mass transport, and geometric optics. Both
researchers and graduate students working on nonlinear differential
equations and their applications will find this to be a useful and
concise resource.
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