منظم بودن مرزهای آزاد در مسائل نوع مانع (مطالعات تحصیلات تکمیلی در ریاضیات)

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, $c1̂$, 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. -- Amazon.com. Model Problems -- Optimal Regularity Of Solutions -- Preliminary Analysis Of The Free Boundary -- Regularity Of The Free Boundary : First Results -- Global Solutions -- Regularity Of The Free Boundary : Uniform Results -- The Singular Set -- Touch With The Fixed Boundary -- The Thin Obstacle Problem. Arshak Petrosyan, Henrik Shahgholian, Nina Uraltseva. Includes Bibliographical References (p. 201-210) And Index. "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, $Ĉ1$, 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."--Amazon.com Mathematicians Petrosyan (Purdue U., Indiana), Henik Shaghgolian (Royal Institute of Technology, Sweden), and Nina Uraltseva (Saint Petersburg State U., Russia) introduce non-experts--especially graduate students just beginning their research--to recent developments and new methods in the regularity of free boundaries, one of the research directions in free boundary problems. Focusing on obstacle-type problems, they cover model problems, the optimal regularity of solutions, preliminary analysis of the free boundary, first results and uniform results of regularity of the free boundary, global solutions, the singular set, touch with the fixed boundary, and the thin obstacle problem. The text can be used in a graduate course, but they warn that the treatment is selective rather than comprehensive or systematic. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)