| 书目名称 | Elliptic Systems of Phase Transition Type | | 编辑 | Nicholas D. Alikakos,Giorgio Fusco,Panayotis Smyrn | | 视频video | | | 概述 | Can be used as principal or supplementary reading for advanced graduate courses on nonlinear analysis or PDEs.Features a self-contained exposition of the existence of connections.Presents a new existe | | 丛书名称 | Progress in Nonlinear Differential Equations and Their Applications | | 图书封面 |  | | 描述 | .This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes – non-orientable objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure not present in the scalar Allen-Cahn equation, which models coexistence of two phases and is related to minimal surfaces. The 1978 De Giorgi conjecture for the scalar problem was settled in a series of papers: Ghoussoub and Gui (2d), Ambrosio and Cabré (3d), Savin (up to 8d), and del Pino, Kowalczyk and Wei (counterexample for 9d and above). This book extends, in various ways, the Caffarelli-Córdoba density estimates that played a major role in Savin‘s proof. It also introduces an alternative method for obtaining pointwise estimates.. Key features and topics of this self-contained, systematic exposition include:..• Resolution of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions...• Preliminary material beginning with the stress-energy tensor, via which monoton | | 出版日期 | Book 2018 | | 关键词 | geodesics; standing waves; maximum principle; point group; crystalline; partial differential equations; or | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-90572-3 | | isbn_ebook | 978-3-319-90572-3Series ISSN 1421-1750 Series E-ISSN 2374-0280 | | issn_series | 1421-1750 | | copyright | Springer Nature Switzerland AG 2018 |
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发表于 2025-3-21 16:04:30
