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| Author | : Luis A. Caffarelli |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 282 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821837842 |
We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.
| Author | : Eduardo V. Teixeira |
| Publisher | : de Gruyter |
| Total Pages | : 312 |
| Release | : 2020-01-13 |
| Genre | : Mathematics |
| ISBN | : 9783110574487 |
This book offers a comprehensive introduction to modern techniques in the study of free boundary problems of diffusive type. Applications of such methods are thoroughly explained by emblematic examples of the theory and several geometric ideas and insights are carefully discussed, making the text both accessible and appealing to a broad readership working in partial differential equations, calculus of variations, and geometric analysis.
| Author | : Bozhidar Velichkov |
| Publisher | : Springer Nature |
| Total Pages | : 249 |
| Release | : 2023-02-24 |
| Genre | : Mathematics |
| ISBN | : 3031132386 |
This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories. This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs.
| Author | : Arshak Petrosyan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 233 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821887947 |
The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.
| Author | : Ioannis Athanasopoulos |
| Publisher | : Routledge |
| Total Pages | : 366 |
| Release | : 2019-11-11 |
| Genre | : Mathematics |
| ISBN | : 1351447149 |
Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.
| Author | : J I Diaz |
| Publisher | : CRC Press |
| Total Pages | : 236 |
| Release | : 1995-04-04 |
| Genre | : Mathematics |
| ISBN | : 9780582256453 |
This research note consists of selected contributions from the 1993 International Conference on "Free Boundary Problems: Theory and Applications." These represent coherent and high-level research in the field of free boundary problems. Topics include mean curvature flows, phase transitions and material sciences, fluid mechanics and combustion problems.
| Author | : A. Bossavit |
| Publisher | : |
| Total Pages | : 334 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Isabel Narra Figueiredo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 462 |
| Release | : 2007-01-11 |
| Genre | : Mathematics |
| ISBN | : 3764377194 |
This book collects refereed lectures and communications presented at the Free Boundary Problems Conference (FBP2005). These discuss the mathematics of a broad class of models and problems involving nonlinear partial differential equations arising in physics, engineering, biology and finance. Among other topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling, in fluid mechanics, in image processing, in financial mathematics or in computations for inter-scale problems.
| Author | : Vladimir Gutlyanskii |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 309 |
| Release | : 2012-04-23 |
| Genre | : Mathematics |
| ISBN | : 1461431913 |
This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.
| Author | : Guido De Philippis |
| Publisher | : Springer Nature |
| Total Pages | : 138 |
| Release | : 2021-03-23 |
| Genre | : Mathematics |
| ISBN | : 303065799X |
This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.
