Degenerate Kolmogorov equations and ergodicity for the stochastic Allen-Cahn equation with logarithmic potential

• Published in: arXiv.org
• Main Authors: Scarpa, Luca, Zanella, Margherita
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 20.06.2022
• Subjects: Ergodic processes

Well-posedness à la Friedrichs is proved for a class of degenerate Kolmogorov equations associated to stochastic Allen-Cahn equations with logarithmic potential. The thermodynamical consistency of the model requires the potential to be singular and the multiplicative noise coefficient to vanish at t...