Variational and diffusion problems in random walk spaces/ José M. Mazón, Marcos Solera-Diana and J. Julián Toledo-Melero

Includes bibliography and index

Random Walks -- The Heat Flow in Random Walk Spaces -- The Total Variation Flow in Random Walk Spaces -- ROF-Models in Random Walk Spaces -- Least Gradient Functions in Random Walk Spaces -- Least Gradient Functions in Random Walk Spaces -- Doubly Nonlinear Nonlocal Diffusion Problems of Leray-Lions Type with Nonlinear Boundary Conditions

This book explores the theory of gradient flows in random walk spaces, establishing a comprehensive framework for various partial differential equations on nonlocal models and weighted graphs. The book delves into specific gradient flows such as the heat flow, total variation flow, and evolution problems of Leray-Lions type with different boundary conditions. It serves as a valuable resource for researchers at the intersection of analysis, geometry, and probability, as well as graduate students interested in these areas.