# Fine regularity of solutions of elliptic partial differential equations

## 書誌事項

Fine regularity of solutions of elliptic partial differential equations

Jan Malý, William P. Ziemer

（Mathematical surveys and monographs, v. 51）

American Mathematical Society, c1997

## 注記

Includes bibliographical references (p. 273-281) and indexes

## 内容説明・目次

The primary objective of this book is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second-order elliptic quasilinear equations in divergence form. The structure of these equations allows coefficients in certain $L^{p}$ spaces, and thus it is known from classical results that weak solutions are locally Holder continuous in the interior. Here it is shown that weak solutions are continuous at the boundary if and only if a Wiener-type condition is satisfied. This condition reduces to the celebrated Wiener criterion in the case of harmonic functions. The work that accompanies this analysis includes the 'fine' analysis of Sobolev spaces and a development of the associated nonlinear potential theory.The term 'fine' refers to a topology of $\mathbf R^{n}$ which is induced by the Wiener condition. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The regularity of the solution is given in terms involving the Wiener-type condition and the fine topology. The case of differential operators with a differentiable structure and $\mathcal C^{1,\alpha}$ obstacles is also developed. The book concludes with a chapter devoted to the existence theory, thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.

Preliminaries Potential theory Quasilinear equations Fine regularity theory Variational inequalities--Regularity Existence theory References Index Notation index.

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## 詳細情報

• NII書誌ID(NCID)
BA31945391
• ISBN
• 0821803352
• LCCN
97011982
• 出版国コード
us
• タイトル言語コード
eng
• 本文言語コード
eng
• 出版地
Providence, R.I.
• ページ数/冊数
xiv, 291 p.
• 大きさ
27 cm
• 分類
• 件名
• 親書誌ID

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