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The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrodinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles.

Offers an exposition on free boundary problems. Free or moving boundary problems appear in many areas of analysis, geometry, and applied mathematics. This book is useful for supplementary reading or as an independent study text. It is also suitable for gra

This book demonstrates the development of the regularity theory of solutions of fully nonlinear elliptic equations. Caffarelli and Cabr 'e offer a detailed presentation of all techniques needed to extend the classic Schauder and Calder 'on-Zygmund regularity theory for linear elliptic equations to a fully nonlinear context. The authors present key ideas and prove all results needed for the theory of viscosity solutions of nonlinear equations, and regularity theory for convex fully nonlinear equations and for fully nonlinear equations with variable coefficients. This book is suitable as a text...