Convex Analysis and Nonlinear Geometric Elliptic EquationsThis graduate-level text examines the areas of convex functions and bodies, global geometric problems and nonlinear elliptic boundary value problems, emphasizing Monge-Ampere equations. |
Contents
2 Supporting Hyperplanes | 14 |
Convex Polyhedra | 24 |
6 Supporting Function | 36 |
Copyright | |
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Convex Analysis and Nonlinear Geometric Elliptic Equations Ilya J. Bakelman No preview available - 1994 |
Common terms and phrases
assume asymptotic cone Bakelman ball Borel subsets boundary value problem bounded domain Clearly closed convex concave consider const constant continuous function converge convex body convex cone convex function convex hypersurface convex polyhedra convex set convex solutions coordinates defined denote derivatives diam G Dirichlet problem domain G elliptic equations En+¹ Euclidean space Euler-Lagrange equation exists exterior normal follows directly fu(x function u(x Gaussian curvature global H₁ Hence holds inf u(x int H interior point K₁ Let u(x linear locally summable Mathem maximum principle mean curvature Minkowski Monge-Ampere equations n-ball n-dimensional nonnegative normal image notation point xo polyhedron positive number proof of Theorem proved quasilinear elliptic equations R₁ satisfy Assumption satisfying the condition set function solutions u(x strictly increasing Subsection supporting function supporting hyperplane u(xo vector vertex vs(x W+(G w+(R₁ μη ав