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Gaussian Capacity Analysis 2018 ed. [Mīkstie vāki]

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  • Formāts: Paperback / softback, 108 pages, height x width: 235x155 mm, weight: 454 g, 1 Illustrations, black and white; IX, 108 p. 1 illus., 1 Paperback / softback
  • Sērija : Lecture Notes in Mathematics 2225
  • Izdošanas datums: 21-Sep-2018
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319950398
  • ISBN-13: 9783319950396
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  • Mīkstie vāki
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Gaussian Capacity Analysis 2018 ed.Palielināt
  • Formāts: Paperback / softback, 108 pages, height x width: 235x155 mm, weight: 454 g, 1 Illustrations, black and white; IX, 108 p. 1 illus., 1 Paperback / softback
  • Sērija : Lecture Notes in Mathematics 2225
  • Izdošanas datums: 21-Sep-2018
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319950398
  • ISBN-13: 9783319950396
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783319950396.html
Keywords:
This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of the Gaussian 1-capacity and the Gaussian Poincaré 1-inequality.  Applications to function spaces and geometric measures are also presented.





This book will be of use to researchers who specialize in potential theory, elliptic differential equations, functional analysis, probability, and geometric measure theory. 
1 Gaussian Sobolev p-Space
1(18)
1.1 Definition and Approximation of W1,p(Gn)
1(7)
1.2 Approximating W1,p(Gn)-Function with Cancellation
8(4)
1.3 Compactness for W1,p(Gn)
12(2)
1.4 Poincare or Log-Sobolev Inequality for W1,2(Gn)
14(5)
2 Gaussian Campanato (p, κ)-Class
19(18)
2.1 Location of Cp,κ(Gn)
19(9)
2.2 Another Look at Cp,κ(Gn) for -p/n ≤ κ < 0
28(9)
3 Gaussian p-Capacity
37(18)
3.1 Gaussian p-Capacity for 1 ≤ p < ∞
37(11)
3.2 Alternative of Gaussian p-Capacity for 1 ≤ p < ∞
48(7)
4 Restriction of Gaussian Sobolev p-Space
55(10)
4.1 Gaussian p-Capacitary-Strong-Type Inequality
55(2)
4.2 Trace Inequality for W1,p(Gn) Under 1 ≤ p ≤ q < ∞
57(2)
4.3 Trace Inequality for W1,p(Gn) Under 0 < q < p < ∞
59(6)
5 Gaussian 1-Capacity to Gaussian ∞-Capacity
65(18)
5.1 Gaussian Co-area Formula and 1-Capacity
65(2)
5.2 Gaussian Poincare 1-Inequality
67(5)
5.3 Ehrhard's Inequality and Gaussian Isoperimetry
72(5)
5.4 Gaussian ∞-Capacity
77(6)
6 Gaussian BV-Capacity
83(20)
6.1 Basics of CapBV(· ; Gn)
83(4)
6.2 Measure Theoretic Nature of CapBV(· ; Gn)
87(4)
6.3 Dual Form of CapBV(· ; Gn)
91(4)
6.4 Gaussian BV Isocapacity and Trace Estimation
95(8)
Bibliography 103(4)
Index 107