An example of singular elliptic stochastic PDE. (English) Zbl 07856281
Summary: We illustrate (some of) the analytic and probabilistic aspects of the theory of regularity structures through the study of the elliptic singular stochastic partial differential equation \((1-\Delta)u=(a+bu)\xi\) on \(\mathbb{T}^d\) in dimensions \(d=1,2\).
MSC:
| 60H17 | Singular stochastic partial differential equations |
| 60L30 | Regularity structures |
| 46F10 | Operations with distributions and generalized functions |
