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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...
The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new.The incentive to explore these spaces arose in the...
Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations...
Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L....
This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday. The articles it contains were born out of the ICMC Summer Meeting on Differential Equations – 2014 Chapter, also dedicated to de...
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