Gradient Flows: In Metric Spaces And In The Space Of Probability Measures

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Springer Science & Business Media, 2005 - 333 Seiten
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This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance.

The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the "metric" theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in non-smooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability.

 

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Inhalt

IV
23
V
26
VI
30
VII
32
VIII
39
IX
42
X
44
XI
45
XLV
182
XLVI
189
XLVII
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XLVIII
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XLIX
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L
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LI
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LII
215

XII
49
XIII
59
XIV
66
XV
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XVI
75
XVII
82
XVIII
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XIX
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XX
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XXI
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XXII
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XXIII
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XXIV
103
XXV
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XXVI
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XXVII
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XXVIII
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XXIX
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XXX
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XXXI
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XXXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
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XXXVII
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XXXVIII
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XXXIX
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XL
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XLI
160
XLII
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XLIII
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XLIV
178
LIII
220
LIV
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LV
229
LVI
231
LVII
232
LVIII
234
LIX
240
LX
244
LXI
246
LXII
254
LXIV
255
LXV
257
LXVI
265
LXVII
267
LXVIII
269
LXIX
272
LXX
276
LXXI
279
LXXII
280
LXXIII
283
LXXIV
284
LXXV
286
LXXVI
295
LXXVII
298
LXXVIII
304
LXXIX
307
LXXX
308
LXXXI
310
LXXXII
314
LXXXIII
321
LXXXIV
331
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Beliebte Passagen

Seite 325 - PL LIONS: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math., 98 (1989), 511-547.
Seite 326 - W. GANGBO AND RJ McCANN, The geometry of optimal transportation, Acta Math., 177 (1996), pp.
Seite 326 - P. Hajlasz, Sobolev spaces on an arbitrary metric space, Potential Anal. 5 (1996), 403-415.

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Über den Autor (2005)

Luigi Ambrosio is Adjunct Professor of Biomaterials at University of Naples "Federico II'. His principal research interest include design and characterisation of polymers and composites for medical applications and tissue engineering, rheology of biological fluids, structural properties of natural tissue, processing of polymers and composites, hydrogels and biodegradable polymers.

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