1. Book Review: Regularity Theory for Elliptic PDE.
- Author
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Mooney, Connor
- Subjects
ELLIPTIC differential equations ,DIRICHLET integrals ,DIFFERENTIAL equations ,APPLIED mathematics ,MINIMAL surfaces ,PARTIAL differential equations ,MAXIMA & minima - Abstract
The article is a book review of "Regularity Theory for Elliptic PDE" by X. Fernández-Real and X. Ros-Oton. The book explores regularity theory for partial differential equations (PDEs) and its applications in various fields such as complex analysis, fluid mechanics, and differential geometry. It discusses the concept of regular solutions and their significance in understanding the behavior of PDEs. The review highlights the importance of regularity theory in solving mathematical problems and its potential impact on various scientific disciplines. The book "Regularity Theory for Elliptic PDE" by Ros-Oton and Fernandez-Real provides an introduction to various topics in elliptic partial differential equations (PDEs). It covers harmonic functions, Schauder estimates, the De Giorgi-Nash-Moser theorem, fully nonlinear elliptic equations, and the obstacle problem. The book presents concise and self-contained proofs of important results, including Caffarelli's results on the smoothness of the free boundary near regular points. It is suitable for graduate students and researchers in applied mathematics, geometry, and PDEs. The book also highlights open questions and the current state of the field. The given text is a list of references to various mathematical papers and books. The references cover a range of topics in the field of calculus of variations, elliptic partial differential equations, and related areas. The authors mentioned in the references have made contributions to the study of regularity, solutions, and properties [Extracted from the article]
- Published
- 2024
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