Dirichlet form associated with the Φ₃⁴ model

2017/03/29 by Rongchan Zhu, Zhu, Rongchan, Xiangchan Zhu +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1703.09987

openalex publication_date 2017/03/29 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We construct the Dirichlet form associated with the dynamical Φ⁴₃ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this classical gradient bilinear form is closable and then by a well-known result its closure is also a quasi-regular Dirichlet form, which means that there exists another (Markov) diffusion process, which also admits the Φ⁴₃ field measure as an invariant (even symmetrizing) measure.

Related

• Dirichlet form approach to diffusions with discontinuous scale
• The dynamical Φ₃⁴ model by an approximation of Laplacian
• The Markov property for φ⁴₃ on the cylinder
• Gradient-type estimates for the dynamic φ⁴₂-model
• Global well-posedness of the dynamic Φ⁴ model in the plane