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

## Maly, Jan; Ziemer, William P.

From 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 book also contains a complete development of regularity of solutions ofvariational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. 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
Librería
Sequitur Books
(Boonsboro, MD, Estados Unidos de America)
Valoración

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 (Mathematical Surveys and Monographs)

Editorial: American Mathematical Society (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356
Librería
Ergodebooks
(RICHMOND, TX, Estados Unidos de America)
Valoración

Descripción American Mathematical Society, 1997. Hardcover. Estado de conservación: New. Nº de ref. de la librería DADAX0821803352

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

Editorial: Amer Mathematical Society (1997)
ISBN 10: 0821803352 ISBN 13: 9780821803356