Ebook: Degenerate Parabolic Equations

Mathematicians have only recently begun to understand the local structure of solutions of degenerate and singular parabolic partial differential equations. The problem originated in the mid '60s with the work of DeGiorgi, Moser, Ladyzenskajia and Uraltzeva. This book will be an account of the developments in this field over the past five years. It evolved out of the 1990-Lipschitz Lectures given by Professor DiBenedetto at the Institut f?r angewandte Mathematik of the University, Bonn.

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Mathematicians have only recently begun to understand the local structure of solutions of degenerate and singular parabolic partial differential equations. The problem originated in the mid '60s with the work of DeGiorgi, Moser, Ladyzenskajia and Uraltzeva. This book will be an account of the developments in this field over the past five years. It evolved out of the 1990-Lipschitz Lectures given by Professor DiBenedetto at the Institut f?r angewandte Mathematik of the University, Bonn.
Content:
Front Matter....Pages i-xv
Notation and function spaces....Pages 1-15
Weak solutions and local energy estimates....Pages 16-40
H?lder continuity of solutions of degenerate parabolic equations....Pages 41-76
H?lder continuity of solutions of singular parabolic equations....Pages 77-116
Boundedness of weak solutions....Pages 117-155
Harnack estimates: the case p>2....Pages 156-183
Harnack estimates and extinction profile for singular equations....Pages 184-214
Degenerate and singular parabolic systems....Pages 215-244
Parabolic p-systems: H?lder continuity of D u ....Pages 245-291
Parabolic p-systems: boundary regularity....Pages 292-315
Non-negative solutions in ? T . The case p>2....Pages 316-333
Non-negative solutions in ? T The case 1<p<2....Pages 334-380
Back Matter....Pages 381-387

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Mathematicians have only recently begun to understand the local structure of solutions of degenerate and singular parabolic partial differential equations. The problem originated in the mid '60s with the work of DeGiorgi, Moser, Ladyzenskajia and Uraltzeva. This book will be an account of the developments in this field over the past five years. It evolved out of the 1990-Lipschitz Lectures given by Professor DiBenedetto at the Institut f?r angewandte Mathematik of the University, Bonn.
Content:
Front Matter....Pages i-xv
Notation and function spaces....Pages 1-15
Weak solutions and local energy estimates....Pages 16-40
H?lder continuity of solutions of degenerate parabolic equations....Pages 41-76
H?lder continuity of solutions of singular parabolic equations....Pages 77-116
Boundedness of weak solutions....Pages 117-155
Harnack estimates: the case p>2....Pages 156-183
Harnack estimates and extinction profile for singular equations....Pages 184-214
Degenerate and singular parabolic systems....Pages 215-244
Parabolic p-systems: H?lder continuity of D u ....Pages 245-291
Parabolic p-systems: boundary regularity....Pages 292-315
Non-negative solutions in ? T . The case p>2....Pages 316-333
Non-negative solutions in ? T The case 1<p<2....Pages 334-380
Back Matter....Pages 381-387
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