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＜E-Book＞
Convex Analysis and Nonlinear Geometric Elliptic Equations / by Ilya J. Bakelman

Edition	1st ed. 1994.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1994
Language	English
Size	XXI, 510 p : online resource
Authors	*Bakelman, Ilya J author SpringerLink (Online service)
Subjects	LCSH:Mathematical analysis LCSH:Geometry, Differential LCSH:Mathematical physics FREE:Analysis FREE:Differential Geometry FREE:Mathematical Methods in Physics FREE:Theoretical, Mathematical and Computational Physics
Notes	I. Elements of Convex Analysis -- 1. Convex Bodies and Hypersurfaces -- 2. Mixed Volumes. Minkowski Problem. Selected Global Problems in Geometric Partial Differential Equations -- II. Geometric Theory of Elliptic Solutions of Monge-Ampere Equations -- 3. Generalized Solutions of N-Dimensional Monge-Ampere Equations -- 4. Variational Problems and Generalized Elliptic Solutions of Monge-Ampere Equations -- 5. Non-Compact Problems for Elliptic Solutions of Monge-Ampere Equations -- 6. Smooth Elliptic Solutions of Monge-Ampere Equations -- III. Geometric Methods in Elliptic Equations of Second Order. Applications to Calculus of Variations, Differential Geometry and Applied Mathematics. -- 7. Geometric Concepts and Methods in Nonlinear Elliptic Euler-Lagrange Equations -- 8. The Geometric Maximum Principle for General Non-Divergent Quasilinear Elliptic Equations Investigations in modem nonlinear analysis rely on ideas, methods and prob­ lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex­ emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com­ plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob­ lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations HTTP:URL=https://doi.org/10.1007/978-3-642-69881-1

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