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  2. Regning og matematisk analyse
  3. Differentialregning & ligninger

Comparison Principles for General Potential Theories and PDEs

Af: H. Blaine Lawson, Kevin R. Payne, F. Reese Harvey, Marco Cirant Engelsk Paperback

Comparison Principles for General Potential Theories and PDEs

Af: H. Blaine Lawson, Kevin R. Payne, F. Reese Harvey, Marco Cirant Engelsk Paperback
Tjek vores konkurrenters priser

An examination of the symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories

In recent years, there has evolved a symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories. This book examines important aspects of this story. One main purpose is to prove comparison principles for nonlinear potential theories in Euclidian spaces straightforwardly from duality and monotonicity under the weakest possible notion of ellipticity. The book also shows how to deduce comparison principles for nonlinear differential operators, by marrying these two points of view, under the correspondence principle.

The authors explain that comparison principles are fundamental in both contexts, since they imply uniqueness for the Dirichlet problem. When combined with appropriate boundary geometries, yielding suitable barrier functions, they also give existence by Perron’s method. There are many opportunities for cross-fertilization and synergy. In potential theory, one is given a constraint set of 2-jets that determines its subharmonic functions. The constraint set also determines a family of compatible differential operators. Because there are many such operators, potential theory strengthens and simplifies the operator theory. Conversely, the set of operators associated with the constraint can influence the potential theory.

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An examination of the symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories

In recent years, there has evolved a symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories. This book examines important aspects of this story. One main purpose is to prove comparison principles for nonlinear potential theories in Euclidian spaces straightforwardly from duality and monotonicity under the weakest possible notion of ellipticity. The book also shows how to deduce comparison principles for nonlinear differential operators, by marrying these two points of view, under the correspondence principle.

The authors explain that comparison principles are fundamental in both contexts, since they imply uniqueness for the Dirichlet problem. When combined with appropriate boundary geometries, yielding suitable barrier functions, they also give existence by Perron’s method. There are many opportunities for cross-fertilization and synergy. In potential theory, one is given a constraint set of 2-jets that determines its subharmonic functions. The constraint set also determines a family of compatible differential operators. Because there are many such operators, potential theory strengthens and simplifies the operator theory. Conversely, the set of operators associated with the constraint can influence the potential theory.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 224
ISBN-13: 9780691243627
Indbinding: Paperback
Udgave:
ISBN-10: 069124362X
Kategori: Differentialregning & ligninger
Udg. Dato: 3 okt 2023
Længde: 16mm
Bredde: 234mm
Højde: 156mm
Forlag: Princeton University Press
Oplagsdato: 3 okt 2023
Forfatter(e): H. Blaine Lawson, Kevin R. Payne, F. Reese Harvey, Marco Cirant
Forfatter(e) H. Blaine Lawson, Kevin R. Payne, F. Reese Harvey, Marco Cirant

Kategori Differentialregning & ligninger

ISBN-13 9780691243627

Sprog Engelsk

Indbinding Paperback

Sider 224

Udgave

Længde 16mm

Bredde 234mm

Højde 156mm

Udg. Dato 3 okt 2023

Oplagsdato 3 okt 2023

Forlag Princeton University Press

Kategori sammenhænge