Overview
- Authors:
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David R. Adams
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Department of Mathematics, University of Kentucky, Lexington, USA
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Lars Inge Hedberg
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Department of Mathematics, Linköping University, Linköping, Sweden
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Table of contents (11 chapters)
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- David R. Adams, Lars Inge Hedberg
Pages 1-16
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- David R. Adams, Lars Inge Hedberg
Pages 17-51
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- David R. Adams, Lars Inge Hedberg
Pages 53-83
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- David R. Adams, Lars Inge Hedberg
Pages 85-127
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- David R. Adams, Lars Inge Hedberg
Pages 129-153
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- David R. Adams, Lars Inge Hedberg
Pages 155-186
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- David R. Adams, Lars Inge Hedberg
Pages 187-214
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- David R. Adams, Lars Inge Hedberg
Pages 215-231
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- David R. Adams, Lars Inge Hedberg
Pages 233-280
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- David R. Adams, Lars Inge Hedberg
Pages 281-303
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- David R. Adams, Lars Inge Hedberg
Pages 305-327
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Back Matter
Pages 329-368
About this book
Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis. In particular, they play a decisive role in the modem theory of partial differential equations (PDE). Potential theory, which grew out of the theory of the electrostatic or gravita tional potential, the Laplace equation, the Dirichlet problem, etc. , had a fundamen tal role in the development of functional analysis and the theory of Hilbert space. Later, potential theory was strongly influenced by functional analysis. More re cently, ideas from potential theory have enriched the theory of those more general function spaces that appear naturally in the study of nonlinear partial differential equations. This book is motivated by the latter development. The connection between potential theory and the theory of Hilbert spaces can be traced back to C. F. Gauss [181], who proved (with modem rigor supplied almost a century later by O. Frostman [158]) the existence of equilibrium potentials by minimizing a quadratic integral, the energy. This theme is pervasive in the work of such mathematicians as D. Hilbert, Ch. -J. de La Vallee Poussin, M. Riesz, O. Frostman, A. Beurling, and the connection was made particularly clear in the work of H. Cartan [97] in the 1940's. In the thesis of J. Deny [119], and in the subsequent work of J. Deny and J. L.
Reviews
"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society
Authors and Affiliations
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Department of Mathematics, University of Kentucky, Lexington, USA
David R. Adams
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Department of Mathematics, Linköping University, Linköping, Sweden
Lars Inge Hedberg
