This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial ...
Casper Beech is a corporate drone. One day his boss sends him in for neural imprinting but a computer glitch loads the wrong file, and Casper is programmed with something that has nothing to do with his job. Instead of learning a new software package, he learns a new way of thinking - a mindset designed by a secret government agency for use in ...
Evans and Oleszek, well-known authors and Washington "insiders," use interviews, congressional documents, and their personal experiences to present thoughtful insights and an original framework that helps students evaluate the congressional reforms of the 1990s.
This volume comprises five extended surveys on the theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a reference on the subject ...
This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, ...
In this volume, the authors demonstrate under some assumptions on $f^+$, $f^-$ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{^+}=f^+dx$ onto $\mu^-=f^-dy$ can be constructed by studying the $p$-Laplacian equation $- \mathrm {div}(\vert DU_p\vert^{p-2}Du_p)=f^+-f^-$ in the limit as $p ...
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