Yang, Meng: Local and Non-Local Dirichlet Forms on the Sierpinski Gasket and the Sierpinski Carpet. 2019
Inhalt
- Preface
- Introduction and Main Results
- Motivation and History
- Goals of the Thesis
- Basic Notions of the SG and the SC
- Statement of the Main Results
- Structure of the Thesis
- Preliminary
- Determination of the Walk Dimension of the SG
- Background and Statement
- The SG and the Sierpinski Graph
- Random Walk on X
- Regular Dirichlet Form on X
- Active Reflected Dirichlet Space (Eref,Frefa)
- Regular Representation of (Eref,Frefa)
- Trace Form on partial X
- Triviality of FK when beta in (beta*,+infty)
- Approximation of Dirichlet Forms on the SG
- Background and Statement
- Proof of Theorem 4.1
- Another Approach of Determination of the Walk Dimension of the SG
- Proof of Theorem 4.2 and 4.3
- Proof of Theorem 4.4
- Proof of Theorem 4.5
- Construction of Local Regular Dirichlet Form on the SG
- Background and Statement
- Resistance Estimates and Good Functions
- Weak Monotonicity Result
- Proof of Theorem 5.1
- Construction of Local Regular Dirichlet Form on the SC
- Background and Statement
- Proof of Lemma 6.1
- Proof of Theorem 6.2
- Resistance Estimates
- Uniform Harnack Inequality
- Weak Monotonicity Results
- One Good Function
- Proof of Theorem 6.3
- Proof of Theorem 6.5
- Proof of Theorem 6.7
- Proof of Theorem 6.8
- Bibliography