| 书目名称 | Functions of Least Gradient |
| 编辑 | Wojciech Górny,José M. Mazón |
| 视频video | |
| 概述 | Stands out as the first book on least gradient functions.Presents both classic and new results on this topic.Features open problems |
| 丛书名称 | Monographs in Mathematics |
| 图书封面 |  |
| 描述 | .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 problems involving functionals with linear growth. Functions which solve the least gradient problem for their own boundary data, which arise naturally in the study of minimal surfaces, are called functions of least gradient...The main part of the book is dedicated to presenting the recent advances in this theory. Among others are presented an Euler–Lagrange characterization of least gradient functions, an anisotropic counterpart of the least gradient problem motivated by an inverse problem in medical imaging, and state-of-the-art results concerning existence, regularity, and structure of solutions. Moreover, the authors present a surprising connection between the least gradient problem and the Monge–Kantorovich optimal transport problem and some of its consequences, and discuss formulations of the least gradient problem in the nonlocal and metric settings. Each chapter is followed by a discussion section concerning oth |
| 出版日期 | Book 2024 |
| 关键词 | Least Gradient Functions; Functions of Bounded Variation; Area-minimizing Sets; Minimal Surface; Anisotr |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-51881-2 |
| isbn_softcover | 978-3-031-51883-6 |
| isbn_ebook | 978-3-031-51881-2Series ISSN 1017-0480 Series E-ISSN 2296-4886 |
| issn_series | 1017-0480 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 18:17:02
