Potential theory on Sierpiński carpets : with applications to uniformization /: with applications to uniformization. (2020)
- Record Type:
- Book
- Title:
- Potential theory on Sierpiński carpets : with applications to uniformization /: with applications to uniformization. (2020)
- Main Title:
- Potential theory on Sierpiński carpets : with applications to uniformization
- Further Information:
- Note: Dimitrios Ntalampekos.
- Other Names:
- Ntalampekos, Dimitrios
- Contents:
- Intro -- Preface -- Contents -- 1 Introduction -- 2 Harmonic Functions on Sierpiński Carpets -- 2.1 Introduction -- 2.2 Basic Assumptions and Notation -- 2.3 Notions of Carpet Modulus -- 2.4 Existence of Paths -- 2.5 Sobolev Spaces on Relative Sierpiński Carpets -- 2.5.1 Discrete Sobolev Spaces -- 2.5.2 Sobolev Spaces -- 2.5.3 Examples -- 2.5.4 Pullback of Sobolev Spaces -- 2.5.5 Properties of Sobolev Spaces -- 2.6 Carpet-Harmonic Functions -- 2.6.1 Definition of Carpet-Harmonic Functions -- 2.6.2 Solution to the Dirichlet Problem -- 2.7 Properties of Harmonic Functions 2.7.1 Continuity and Maximum Principle -- 2.7.2 Uniqueness and Comparison Principle -- 2.7.3 Continuous Boundary Data -- 2.7.4 A Free Boundary Problem -- 2.8 The Caccioppoli Inequality -- 2.9 Harnack's Inequality and Consequences -- 2.9.1 Harnack's Inequality -- 2.9.2 Strong Maximum Principle -- 2.10 Equicontinuity and Convergence -- 3 Uniformization of Sierpiński Carpets by Square Carpets -- 3.1 Introduction -- 3.1.1 Results -- 3.1.2 Organization of the Chapter -- 3.2 Notation and Terminology -- 3.3 Preliminaries -- 3.3.1 Quasisymmetric and Quasiconformal Maps -- 3.3.2 Modulus 3.3.3 Existence of Paths -- 3.4 The Function u -- 3.4.1 Background on Carpet-Harmonic Functions -- 3.4.2 The Free Boundary Problem -- 3.5 The Level Sets of u -- 3.6 The Conjugate Function v -- 3.7 Definition of f -- 3.8 Injectivity of f -- 3.9 Regularity of f and f-1 -- 3.10 Carpet Modulus Estimates -- 3.11 QuasisymmetricIntro -- Preface -- Contents -- 1 Introduction -- 2 Harmonic Functions on Sierpiński Carpets -- 2.1 Introduction -- 2.2 Basic Assumptions and Notation -- 2.3 Notions of Carpet Modulus -- 2.4 Existence of Paths -- 2.5 Sobolev Spaces on Relative Sierpiński Carpets -- 2.5.1 Discrete Sobolev Spaces -- 2.5.2 Sobolev Spaces -- 2.5.3 Examples -- 2.5.4 Pullback of Sobolev Spaces -- 2.5.5 Properties of Sobolev Spaces -- 2.6 Carpet-Harmonic Functions -- 2.6.1 Definition of Carpet-Harmonic Functions -- 2.6.2 Solution to the Dirichlet Problem -- 2.7 Properties of Harmonic Functions 2.7.1 Continuity and Maximum Principle -- 2.7.2 Uniqueness and Comparison Principle -- 2.7.3 Continuous Boundary Data -- 2.7.4 A Free Boundary Problem -- 2.8 The Caccioppoli Inequality -- 2.9 Harnack's Inequality and Consequences -- 2.9.1 Harnack's Inequality -- 2.9.2 Strong Maximum Principle -- 2.10 Equicontinuity and Convergence -- 3 Uniformization of Sierpiński Carpets by Square Carpets -- 3.1 Introduction -- 3.1.1 Results -- 3.1.2 Organization of the Chapter -- 3.2 Notation and Terminology -- 3.3 Preliminaries -- 3.3.1 Quasisymmetric and Quasiconformal Maps -- 3.3.2 Modulus 3.3.3 Existence of Paths -- 3.4 The Function u -- 3.4.1 Background on Carpet-Harmonic Functions -- 3.4.2 The Free Boundary Problem -- 3.5 The Level Sets of u -- 3.6 The Conjugate Function v -- 3.7 Definition of f -- 3.8 Injectivity of f -- 3.9 Regularity of f and f-1 -- 3.10 Carpet Modulus Estimates -- 3.11 Quasisymmetric Uniformization -- 3.12 Equivalence of Square and Round Carpets -- 3.13 A Test Function -- References -- Index … (more)
- Publisher Details:
- Cham : Springer
- Publication Date:
- 2020
- Extent:
- 1 online resource
- Subjects:
- 515/.96
Potential theory (Mathematics)
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9783030508050
3030508056 - Related ISBNs:
- 3030508048
9783030508043 - Notes:
- Note: Includes bibliographical references and index.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.550369
- Ingest File:
- 03_167.xml