Bosnić, Filip: Models of degenerate random conductances with stable-like jumps. 2020
Inhalt
- Introduction
- Preliminaries
- Notation
- Inequalities
- Bochner integral
- Dirichlet forms
- Markov processes
- Volume regularity of Zn
- Symmetric jump type forms
- Generalized Mosco convergence
- List of properties
- Deterministic degenerate energy forms of jump type
- Assumptions and main ideas
- Weak solution and testing lemma
- Parabolic Moser iteration
- Iteration preparations
- Iteration for negative exponents
- Iteration for small positive exponents
- Connecting positive and negative exponents
- Weighted Poincaré inequality
- Energy estimate for logu
- Weak L1 estimates on logu
- Lemma of Bombieri and Giusti
- Weak Harnack inequality
- Hölder regularity estimate
- Exit time estimates and conservativeness
- Estimate of the expected exit time
- Survival estimate and conservativeness
- Truncation and survival probabilities
- Local Poincaré-Sobolev inequality
- Long-range random conductance model
- Motivation and definitions
- Symmetrized ergodic conductance
- Estimates on spatial averages
- Functional inequalities in ergodic environment
- Energy density of cutoff functions
- Weak Harnack inequality and Hölder regularity
- Exit time estimates
- i.i.d. conductance
- Basic estimates
- Sobolev inequality
- Poincare inequality
- Lower estimates on the kernel
- Energy density of cutoff functions
- Tail estimates
- Weak Harnack inequality and Hölder regularity
- Exit time estimates
- Convergence results