Schauder estimates for fractional Laplacians and non-local, one-dimensional singular SPDEs

We examine in this article the one-dimensional, non-local, singular SPDE \begin{equation*} \partial_t u \;=\; -\, (-\Delta)^{1/2} u \,-\, \sinh(\gamma u) \,+\, \xi\;, \end{equation*} where $\gamma\in \mathbb{R}$, $(-\Delta)^{1/2}$ is the fractional Laplacian of order $1/2$, $\xi$ the space-time whit...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on mathematical analysis 2022
Main Authors: Chiarini, Leandro, Landim, Claudio
Format: Article
Language:English
Subjects:
Mathematics
Probability
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We examine in this article the one-dimensional, non-local, singular SPDE \begin{equation*} \partial_t u \;=\; -\, (-\Delta)^{1/2} u \,-\, \sinh(\gamma u) \,+\, \xi\;, \end{equation*} where $\gamma\in \mathbb{R}$, $(-\Delta)^{1/2}$ is the fractional Laplacian of order $1/2$, $\xi$ the space-time white noise in $\mathbb{R} \times \mathbb{T}$, and $\mathbb{T}$ the one-dimensional torus. We show that for $0
ISSN:0036-1410
DOI:10.1137/20M1382829