Titlebook: Convex Analysis and Nonlinear Geometric Elliptic Equations; Ilya J. Bakelman Book 1994 Springer-Verlag Berlin Heidelberg 1994 Convex analy

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Convex Bodies and HypersurfacesThe concept of a convex set can be introduced in any linear space .. A set . in . is called . if the line segment . is contained in . for any elements a, ., i.e. . for any . and any . ∈ [0,1].

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Mixed Volumes. Minkowski Problem. Selected Global Problems in Geometric Partial Differential EquatioLet . be a (. + 1)-dimensional Euclidean vector space. We denote by E. the (n + 1)-dimensional Euclidean point space associated with . (see §1). Then every vector . ∈ . generates a parallel translation . in the following way: for any point . ∈ ., where . is the terminal point of the vector ..

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The Geometric Maximum Principle for General Non-Divergent Quasilinear Elliptic EquationsIn this chapter we present the geometric maximum principles for solutions . of the elliptic Dirichlet problem .where . is a bounded domain in the Euclidean space . and . is a closed continuous hypersurface in .. We assume that ..

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Victorian Poetry and Modern Lifections is the extension of Monge-Ampere operators to the class of all general convex functions. We study in detail the properties of the normal mapping and .-curvature of convex functions and then investigate the solvability of the Dirichlet problem for weak and generalized elliptic solutions togeth

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Victorian Poetry and Modern Lifelute minimum of these variational problems turns out to be a generalized solution of the corresponding Monge-Ampere equations. In this chapter we study explicitly the main variational problem connected with the Monge- Ampere equation . and also consider generalizations of it.

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Virginia Woolf and the Modern Sublime: ,with prescribed Gaussian curvature . in (. + l)-dimensional Euclidean space .. Here . is a positive continuous function on the unit hypersphere . ⊂ ., which is centered at the origin of .. The Minkowski problem is the problem of existence and uniqueness of a closed convex hypersurface . with Gaussia

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