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Geometric approach to evolution problems in metric spaces


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  • Product Description

This PhD thesis contains four chapters where research material on a range of different topics is presented. The used and developed techniques fall within the scope of analysis, probability and metric geometry, while a significant part of the manuscript contributes to the optimal transportation theory. In the second chapter the product formulas for semigroups induced by convex functionals in general CAT(0) spaces are proven---extending the classical results in Hilbert spaces. Third chapter contains a treatment of the non-symmetric Fokker-Planck equation as a flow on the Wasserstein-2 space of probability measures---we prove that its semigroup of solutions possesses similar properties to the properties of the gradient flow semigroups. In the forth chapter a general theory of maximal monotone operators and the induced flows on Wasserstein-2 spaces over Euclidean spaces is developed. This theory generalizes the theory of gradient flows by Ambrosio-Gigli-Savaré. In the fifth chapter the existence of an invariant measure for stochastic delay equations is proven. The diffusion coefficient has an exponentially stable delay, and is only assumed to be locally Lipschitz and bounded.

Product Specifications
SKU :COC93482
AuthorIgor Stojkovi?
Number of Pages240
Publishing Year2011-09-01T00:00:00.000
Edition1 st
Book TypeReal analysis, real variables
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-08-14 00:00:00