Minimal Surfaces and Functions of Bounded Variation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Minimal Surfaces and Functions of Bounded Variation write by Giusti. This book was released on 2013-03-14. Minimal Surfaces and Functions of Bounded Variation available in PDF, EPUB and Kindle. The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].
Minimal Surfaces and Functions of Bounded Variation
Minimal Surfaces and Functions of Bounded Variation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Minimal Surfaces and Functions of Bounded Variation write by E. Giusti. This book was released on 1977. Minimal Surfaces and Functions of Bounded Variation available in PDF, EPUB and Kindle.
Boundary Value Problems of Mathematical Physics
Boundary Value Problems of Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Boundary Value Problems of Mathematical Physics write by Ivar Stakgold. This book was released on 2000. Boundary Value Problems of Mathematical Physics available in PDF, EPUB and Kindle.
Functions of Bounded Variation and Their Fourier Transforms
Functions of Bounded Variation and Their Fourier Transforms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Functions of Bounded Variation and Their Fourier Transforms write by Elijah Liflyand. This book was released on 2019-03-06. Functions of Bounded Variation and Their Fourier Transforms available in PDF, EPUB and Kindle. Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series.
Minimal Surfaces II
Minimal Surfaces II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Minimal Surfaces II write by Ulrich Dierkes. This book was released on 2013-03-14. Minimal Surfaces II available in PDF, EPUB and Kindle. Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can also be useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory for nonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.
