Gaussian capacity analysis

✍ Scribed by Liu L

• Publisher: Springer
• Year: 2018
• Tongue: English
• Leaves: 115
• Series: Springer Lecture notes in mathematics 2225
• Category: Library

✦ Table of Contents

Preface......Page 6
Contents......Page 10
1.1 Definition and Approximation of W1,p(=G"80 n)......Page 11<br> 1.2 Approximating W1,p(=G"80 n)-Function with Cancellation......Page 18
1.3 Compactness for W1,p(=G"80 n)......Page 22<br> 1.4 Poincaré or Log-Sobolev Inequality for W1,2(=G"80 n)......Page 24
2.1 Location of Cp,κ(=G"80 n)......Page 29<br> 2.2 Another Look at Cp,κ(=G"80 n) for -pnκ<0......Page 38
3.1 Gaussian p-Capacity for 1p<∞......Page 46
3.2 Alternative of Gaussian p-Capacity for 1p<∞......Page 57
4.1 Gaussian p-Capacitary-Strong-Type Inequality......Page 63
4.2 Trace Inequality for W1,p(=G"80 n) Under1pq<∞......Page 65<br> 4.3 Trace Inequality for W1,p(=G"80 n) Under0<q<p<∞......Page 67
5.1 Gaussian Co-area Formula and 1-Capacity......Page 73
5.2 Gaussian Poincaré 1-Inequality......Page 75
5.3 Ehrhard's Inequality and GaussianIsoperimetry......Page 80
5.4 Gaussian ∞-Capacity......Page 85
6.1 Basics of CapBV(·;=G"80 n)......Page 91<br> 6.2 Measure Theoretic Nature of CapBV(·;=G"80 n)......Page 95
6.3 Dual Form of CapBV(·;=`G"80 n)......Page 99
Bibliography......Page 103
Index......Page 114