# Fine Regularity of Solutions of Elliptic Partial Differential Equations (Mathematical Surveys and Monographs)

## Jan Maly; William P. Ziemer

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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.

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## 1.Fine Regularity of Solutions of Elliptic Partial Differential Equations (Mathematical Surveys and Monographs)

Editorial: American Mathematical Society (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356
Nuevos Tapa dura Cantidad: > 20
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Sequitur Books
(Boonsboro, MD, Estados Unidos de America)
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Descripción American Mathematical Society, 1997. Hardcover. Estado de conservación: New. Brand new. We distribute directly for the publisher. 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 Hölder 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. Nº de ref. de la librería 1006230121

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## 2.Fine Regularity of Solutions of Elliptic Partial Differential Equations (Hardback)

Editorial: American Mathematical Society, United States (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
The Book Depository US
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 1997. Hardback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AAN9780821803356

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## 3.Fine Regularity of Solutions of Elliptic Partial Differential Equations (Hardback)

Editorial: American Mathematical Society, United States (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
The Book Depository
(London, Reino Unido)
Valoración

Descripción American Mathematical Society, United States, 1997. Hardback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AAN9780821803356

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## 4.Fine Regularity of Solutions of Elliptic Partial Differential Equations

Editorial: American Mathematical Society
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
THE SAINT BOOKSTORE
(Southport, Reino Unido)
Valoración

Descripción American Mathematical Society. Hardback. Estado de conservación: new. BRAND NEW, Fine Regularity of Solutions of Elliptic Partial Differential Equations, Jan Maly, William P. Ziemer, 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. Nº de ref. de la librería B9780821803356

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## 5.Fine Regularity of Solutions of Elliptic Partial Differential Equations (Mathematical Surveys and Mo

Editorial: American Mathematical Society (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
Murray Media
(North Miami Beach, FL, Estados Unidos de America)
Valoración

Descripción American Mathematical Society, 1997. Hardcover. Estado de conservación: New. Nº de ref. de la librería P110821803352

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## 6.Fine Regularity of Solutions of Elliptic Partial Differential Equations (Mathematical Surveys and Monographs)

Editorial: American Mathematical Society (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
Ergodebooks
(RICHMOND, TX, Estados Unidos de America)
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Descripción American Mathematical Society, 1997. Hardcover. Estado de conservación: New. Nº de ref. de la librería DADAX0821803352

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## 7.Fine Regularity of Solutions of Elliptic Partial Differential Equations (Mathematical Surveys and Monographs)

Editorial: American Mathematical Society (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
Irish Booksellers
(Rumford, ME, Estados Unidos de America)
Valoración

Descripción American Mathematical Society, 1997. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería 0821803352

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## 8.Fine Regularity of Solutions of Elliptic Partial Differential Equations (Mathematical Surveys and Monographs)

Editorial: American Mathematical Society
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
Cloud 9 Books
(Wellington, FL, Estados Unidos de America)
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Descripción American Mathematical Society. Hardcover. Estado de conservación: New. 0821803352 New Condition. Nº de ref. de la librería NEW6.3211355

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## 9.Fine Regularity of Solutions of Elliptic Partial Differential Equations (Mathematical Surveys and Monographs)

Editorial: Amer Mathematical Society (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
Revaluation Books
(Exeter, Reino Unido)
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Descripción Amer Mathematical Society, 1997. Hardcover. Estado de conservación: Brand New. 291 pages. 10.50x7.50x1.00 inches. In Stock. Nº de ref. de la librería __0821803352

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## 10.Fine Regularity Of Solutions Of Elliptic Partial Differential Equations

ISBN 10: 0821803352 ISBN 13: 9780821803356