Gubinelli, Massimiliano; Hofmanová, Martina: Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space. In: Communications in Mathematical Physics. Jg.368 H. 3. 2019, S. 1201-1266
Inhalt
- 2 Preliminaries
- 2.1 Weighted Besov spaces
- 2.2 Interpolation
- 2.3 Localization operators
- 2.4 Elliptic Schauder estimates
- 2.5 Elliptic coercive estimates
- 2.6 Parabolic Schauder estimates
- 2.7 Parabolic coercive estimates
- 2.8 Paracontrolled calculus
- 3 Probabilistic Analysis
- 4 Elliptic Φ44 Model
- 5 Elliptic Φ45 Model
- 5.1 Decomposition into simpler equations
- 5.2 Including the localizers
- 5.3 Bound for φ in mathscrC α(ρ)
- 5.4 Bound for φ in mathscrC 12+α(ρ32+α)
- 5.5 Bound for in mathscrC 1+α(ρ2+α)
- 5.6 Bound for ψ in mathscrC 2+γ(ρ3+γ)
- 5.7 Bound for ψ in Linfty(ρ)
- 5.8 Existence
- 6 Parabolic Φ42 Model
- 7 Parabolic Φ43 Model
- 8 Uniqueness for the Parabolic Models
- 9 Coming Down from Infinity
- 9.1 Interpolation and localization
- 9.2 Weighted Schauder estimates
- 9.3 Weighted coercive estimate
- 9.4 Proof of Theorem 9.1
- Acknowledgements.
- A Auxiliary PDE Results
- B Refined Schauder Estimates
- References