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Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
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Convex Analysis and Nonlinear Geometric Elliptic Equations (Paperback, Softcover reprint of the original 1st ed. 1994)
Loot Price: R1,631
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Convex Analysis and Nonlinear Geometric Elliptic Equations (Paperback, Softcover reprint of the original 1st ed. 1994)
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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."
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