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© 2018

Gaussian Capacity Analysis

Benefits

  • The first book presenting a systematic study of the Sovolev/BV capacity theory in the Gaussian setting

  • Provides fundamental material for a cross-disciplinary field

  • Provides interesting applications in the geometry of Gaussian space

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2225)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 1-18
  3. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 19-35
  4. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 37-53
  5. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 55-64
  6. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 65-82
  7. Liguang Liu, Jie Xiao, Dachun Yang, Wen Yuan
    Pages 83-101
  8. Back Matter
    Pages 103-108

About this book

Introduction

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.  

Keywords

Gaussian Measure Gaussian Sobolev Function Gaussian BV Function Poincaré Inequality Gaussian Isoperimetry

Authors and affiliations

  1. 1.School of MathematicsRenmin University of ChinaBeijingChina
  2. 2.Department Mathematics & StatisticsMemorial UniversitySt. John’s, Newfoundland and LabradorCanada
  3. 3.Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  4. 4.Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical SciencesBeijing Normal UniversityBeijingChina

Bibliographic information

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