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This book is devoted to the least gradient problem and its variants. The least gradient problem concerns minimization of the total variation of a function with prescribed values on the boundary of a Lipschitz domain. It is the model problem for studying minimization...
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...
This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them. These...
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