عنوان

A first course in Sobolev spaces /

شابک

1470429217

شابک

9781470429218

عنوان اصلي

A first course in Sobolev spaces /

نام عام مواد

[Book]

نام نخستين پديدآور

Giovanni Leoni.

وضعيت ويراست

Second edition.

محل نشرو پخش و غیره

Providence, Rhode Island :

نام ناشر، پخش کننده و غيره

American Mathematical Society,

تاریخ نشرو بخش و غیره

[2017]

نام خاص و کميت اثر

xxii, 734 pages ;

ابعاد

27 cm.

عنوان فروست

Graduate studies in mathematics ;

مشخصه جلد

181

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

Monotone functions -- Functions of bounded pointwise variation -- Absolutely continuous functions -- Decreasing rearrangement -- Curves -- Lebesgue-Stieltjes measures -- Functions of bounded variation and Sobolev functions -- The infinite-dimensional case -- Change of variables and the divergence theorem -- Distributions -- Sobolev spaces -- Sobolev spaces: embeddings -- Sobolev spaces: further properties -- Functions of bounded variation -- Sobolev spaces: symmetrization -- Interpolation of Banach spaces -- Besov spaces -- Sobolev spaces: traces.

بدون عنوان

0

متن يادداشت

This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue-Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.

موضوع مستند نشده

Sobolev spaces.

موضوع مستند نشده

Sobolev spaces.

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Leoni, Giovanni,1967-

تاريخ عمليات

20200823025738.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y