An Introduction to Sobolev Spaces and Interpolation Spaces

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Springer Science & Business Media, May 26, 2007 - Mathematics - 219 pages
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After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.

 

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Contents

II
1
III
9
IV
15
V
17
VI
21
VII
26
VIII
33
IX
37
XXVI
123
XXVII
127
XXVIII
130
XXIX
137
XXX
141
XXXI
144
XXXII
149
XXXIII
155

X
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XI
49
XII
52
XIII
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XIV
64
XV
69
XVI
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XVII
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XVIII
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XIX
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XX
93
XXI
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XXII
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XXIII
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XXIV
114
XXV
119
XXXIV
159
XXXV
162
XXXVI
165
XXXVII
169
XXXVIII
173
XXXIX
177
XL
182
XLI
191
XLII
195
XLIII
199
XLIV
204
XLV
209
XLVI
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XLVII
215
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About the author (2007)

Luc Tartar studied at Ecole Polytechnique in Paris, France, 1965-1967, where he was taught by Laurent Schwartz and Jacques-Louis Lions in mathematics, and by Jean Mandel in continuum mechanics.

He did research at Centre National de la Recherche Scientifique, Paris, France, 1968-1971, working under the direction of Jacques-Louis Lions for his thèse d'état, 1971.

He taught at Université Paris IX-Dauphine, Paris, France, 1971-1974, at University of Wisconsin, Madison, WI, 1974-1975, at Université de Paris-Sud, Orsay, France, 1975-1982.

He did research at Commissariat à l'Energie Atomique, Limeil, France, 1982-1987.

In 1987, he was elected Correspondant de l'Académie des Sciences, Paris, in the section Mécanique.

Since 1987 he has been teaching at Carnegie Mellon University, Pittsburgh, PA, where he has been University Professor of Mathematics since 1994.

Partly in collaboration with François Murat, he has specialized in the development of new mathematical tools for solving the partial differential equations of continuum mechanics (homogenization, compensated compactness, H-measures), pioneering the study of microstructures compatible with the partial differential equations describing the physical balance laws, and the constitutive relations.

He likes to point out the defects of many of the models which are used, as a natural way to achieve the goal of improving our understanding of mathematics and of continuum mechanics.

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