Gradient Flows: In Metric Spaces and in the Space of Probability MeasuresSpringer Science & Business Media, 28.01.2005 - 333 Seiten This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein 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 ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability. |
Inhalt
IV | 23 |
V | 26 |
VI | 30 |
VII | 32 |
VIII | 39 |
IX | 42 |
X | 44 |
XI | 45 |
XLV | 182 |
XLVI | 189 |
XLVII | 194 |
XLVIII | 201 |
XLIX | 202 |
L | 205 |
LI | 209 |
LII | 215 |
XII | 49 |
XIII | 59 |
XIV | 66 |
XV | 71 |
XVI | 75 |
XVII | 82 |
XVIII | 84 |
XIX | 89 |
XX | 92 |
XXI | 93 |
XXII | 97 |
XXIII | 99 |
XXIV | 103 |
XXV | 105 |
XXVI | 106 |
XXVII | 109 |
XXVIII | 113 |
XXIX | 118 |
XXX | 121 |
XXXI | 124 |
XXXII | 128 |
XXXIII | 133 |
XXXIV | 135 |
XXXV | 139 |
XXXVI | 142 |
XXXVII | 146 |
XXXVIII | 148 |
XXXIX | 151 |
XL | 158 |
XLI | 160 |
XLII | 167 |
XLIII | 169 |
XLIV | 178 |
LIII | 220 |
LIV | 227 |
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 |
331 | |
Andere Ausgaben - Alle anzeigen
Gradient Flows: In Metric Spaces and in the Space of Probability Measures Luigi Ambrosio,Nicola Gigli,Giuseppe Savare Eingeschränkte Leseprobe - 2006 |
Häufige Begriffe und Wortgruppen
A-convex absolutely continuous curves apply approximate differential argument Banach space Borel bounded Chapter characterization choose compact condition consider constant speed geodesic continuity equation convex functionals convexity Assumption Corollary curves of maximal Cyl(X defined Definition denote discrete solutions dµ(x estimates exists finite dimensional follows formula Fréchet subdifferential geodesically convex geodesics gradient flow Hilbert space holds induced interpolation Lemma lim inf lim sup Lipschitz lower semicontinuous maximal slope metric derivative metric space monotone narrowly converging nonnegative norm obtain optimal plan optimal transport map particular Pp(X probability measures Proof Proposition prove Rd Rd recall regular Remark result Section sequence strong subdifferential strong upper gradient subdifferential subset Theorem topology uniformly integrable unique variational inequalities vector field velocity Wasserstein distance yields µ Є µ¹ µ² µ³ π¹
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.