Variational and Diffusion Problems in Random Walk Spaces
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Beschreibung
This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research.
Variational and Diffusion Problems in Random Walk Spaces will be of interest to researchers at the interface between analysis, geometry, and probability, as well as to graduate students interested in exploring these areas.
This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research.
Variational and Diffusion Problems in Random Walk Spaces will be of interest to researchers at the interface between analysis, geometry, and probability, as well as to graduate students interested in exploring these areas.
Presents the latest developments of the theory of gradient flows in random walk spaces Unifies into a broad framework a wide variety of partial differential equations on nonlocal models and weighted graphs Explores state-of-the-art research occuring at the interface between analysis, geometry, and probability
Autor*in
José M. Mazón
Themen in »Variational and Diffusion Problems in Random Walk Spaces«
Diffusion problems Diffusion processes Variational problems Gradient flows Random walk spaces Total variation flow Olivier-Ricci curvature ROF-models Least gradient functions Leray-Lions type Doubly nonlinear nonlocal diffusion problems Neumann boundary conditions