Olivier Druet's Books

The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

Sharp Sobolev Inequalities and Related Problems

By: Olivier Druet,Emmanuel Hebey

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The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

Sharp Sobolev Inequalities and Related Problems

By: Olivier Druet,Emmanuel Hebey

Function theory and Sobolev inequalities have been the target of investigation for many years. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The $AB$ programme is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. This text summarizes the results of contemporary research and gives an up-to-date report on the field.

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Page Count

113

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821829890

ISBN 13

9780821829899

Blow-up Theory for Elliptic PDEs in Riemannian Geometry

By: Olivier Druet,Emmanuel Hebey,Frédéric Robert

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Blow-up Theory for Elliptic PDEs in Riemannian Geometry

By: Olivier Druet,Emmanuel Hebey,Frédéric Robert

Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.

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Page Count

227

Publisher

Princeton University Press

Published Date

ISBN 10

1400826160

ISBN 13

9781400826162

The Lin-Ni's Problem for Mean Convex Domains

By: Olivier Druet,Frédéric Robert,Juncheng Wei

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The Lin-Ni's Problem for Mean Convex Domains

By: Olivier Druet,Frédéric Robert,Juncheng Wei

The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.

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Page Count

118

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821869094

ISBN 13

9780821869093

The History of the Paris Commune of 1871

By: Prosper-Olivier Lissagaray

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The History of the Paris Commune of 1871

By: Prosper-Olivier Lissagaray

In 1871, the working class of Paris, incensed by their lack of political power and tired of being exploited, seized control of the capital. This book is the outstanding history of the Commune, theheroic battles fought in its defence, and the bloody massacre that ended the uprising. Its author, Lissagaray, was a young journalist who not only saw the events recounted here first-hand, but fought for the Commune on the barricades. He spent the next twenty-five years researching and writing this history, which refutes the slanders levelled at the Communards by the ruling classes and is a vivid and valuable study in urban political revolution, one that retains its power to inspire to this day. This revised edition, translated by Eleanor Marx, includes a foreword by the writer and publisher Eric Hazan.

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Page Count

657

Publisher

Verso Books

Published Date

ISBN 10

1789601274

ISBN 13

9781789601275

History of the Paris Commune of 1871

By: Prosper-Olivier Lissagaray

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History of the Paris Commune of 1871

By: Prosper-Olivier Lissagaray

The classic history of the Paris Commune In 1871, the working class of Paris, incensed by their lack of political power and tired of beingexploited, seized control of the capital. This book is the outstanding history of the Commune, theheroic battles fought in its defence, and the bloody massacre that ended the uprising. Its author,Lissagaray, was a young journalist who not only saw the events recounted here first-hand, butfought for the Commune on the barricades. He spent the next twenty-five years researching andwriting this history, which refutes the slanders levelled at the Communards by the ruling classesand is a vivid and valuable study in urban political revolution, one that retains its power to inspireto this day. This revised edition includes a foreword by the writer and publisher Eric Hazan.

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Page Count

465

Publisher

Verso Books

Published Date

ISBN 10

1844677761

ISBN 13

9781844677764

Blow-up Theory for Elliptic PDEs in Riemannian Geometry

By: Olivier Druet,Emmanuel Hebey,Frédéric Robert

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Blow-up Theory for Elliptic PDEs in Riemannian Geometry

By: Olivier Druet,Emmanuel Hebey,Frédéric Robert

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Page Count

227

Publisher

Princeton University Press

Published Date

ISBN 10

1400826160

ISBN 13

9781400826162

The Lin-Ni's Problem for Mean Convex Domains

By: Olivier Druet,Frédéric Robert,Juncheng Wei

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The Lin-Ni's Problem for Mean Convex Domains

By: Olivier Druet,Frédéric Robert,Juncheng Wei

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Page Count

118

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821869094

ISBN 13

9780821869093

The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

Sharp Sobolev Inequalities and Related Problems

By: Olivier Druet,Emmanuel Hebey

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The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

Sharp Sobolev Inequalities and Related Problems

By: Olivier Druet,Emmanuel Hebey

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Page Count

113

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821829890

ISBN 13

9780821829899

The AB Program in Geometric Analysis

Sharp Sobolev Inequalities and Related Problems

By: Olivier Druet,F R Gantmakher

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The AB Program in Geometric Analysis

Sharp Sobolev Inequalities and Related Problems

By: Olivier Druet,F R Gantmakher

Euclidean background Statement of the $AB$ program Some historical motivations The $H^2_1$-inequality--Part I The $H^2_1$-inequality--Part II PDE methods The isoperimetric inequality The $H^p_1$-inequalities, $1

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ISBN 10

1470403595

ISBN 13

9781470403591

Book's by Olivier Druet

The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

Blow-up Theory for Elliptic PDEs in Riemannian Geometry

Blow-up Theory for Elliptic PDEs in Riemannian Geometry

The Lin-Ni's Problem for Mean Convex Domains

The Lin-Ni's Problem for Mean Convex Domains

The History of the Paris Commune of 1871

The History of the Paris Commune of 1871

History of the Paris Commune of 1871

History of the Paris Commune of 1871

Blow-up Theory for Elliptic PDEs in Riemannian Geometry

Blow-up Theory for Elliptic PDEs in Riemannian Geometry

The Lin-Ni's Problem for Mean Convex Domains

The Lin-Ni's Problem for Mean Convex Domains

The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

The AB Program in Geometric Analysis

The AB Program in Geometric Analysis

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