By Cristian Gutierrez
Now in its moment variation, this monograph explores the Monge-Ampère equation and the most recent advances in its examine and applications. It offers an basically self-contained systematic exposition of the idea of vulnerable ideas, together with regularity effects by means of L. A. Caffarelli. The geometric elements of this thought are under pressure utilizing recommendations from harmonic research, akin to masking lemmas and set decompositions. An attempt is made to give entire proofs of all theorems, and examples and workouts are provided to extra illustrate very important concepts. the various themes thought of contain generalized options, non-divergence equations, go sections, and convex solutions. New to this version is a bankruptcy at the linearized Monge-Ampère equation and a bankruptcy on inside Hölder estimates for moment derivatives. Bibliographic notes, up to date and increased from the 1st version, are incorporated on the finish of each bankruptcy for additional studying on Monge-Ampère-type equations and their different functions within the components of differential geometry, the calculus of diversifications, optimization difficulties, optimum mass shipping, and geometric optics. either researchers and graduate scholars engaged on nonlinear differential equations and their purposes will locate this to be an invaluable and concise resource.
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Extra resources for The Monge-Ampère Equation (Progress in Nonlinear Differential Equations and Their Applications)
The Monge-Ampère Equation (Progress in Nonlinear Differential Equations and Their Applications) by Cristian Gutierrez