Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Analysis of PDEs

arXiv:2207.08428 (math)
[Submitted on 18 Jul 2022 (v1), last revised 26 Aug 2022 (this version, v2)]

Title:Solution theory to semilinear stochastic equations of Schrödinger type on curved spaces I -- Operators with uniformly bounded coefficients

Authors:Alessia Ascanelli, Sandro Coriasco, André Süß
View PDF
Abstract:We study the Cauchy problem for Schrödinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy data, and on the spectral measure associated with the noise, such that the Cauchy problem admits a unique function-valued mild solution in the sense of Da Prato and Zabczyc.
Comments: 10 pages. Minor modification and extension of the introduction. Misprints correction. arXiv admin note: text overlap with arXiv:2010.07087
Subjects: Analysis of PDEs (math.AP); Probability (math.PR)
MSC classes: Primary: 35R60, 60H15, Secondary: 35Q40
Cite as: arXiv:2207.08428 [math.AP]
  (or arXiv:2207.08428v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2207.08428

Submission history

From: Sandro Coriasco [view email]
[v1] Mon, 18 Jul 2022 08:24:33 UTC (17 KB)
[v2] Fri, 26 Aug 2022 14:17:18 UTC (18 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.AP
< prev   |   next >
new | recent | 2022-07
Change to browse by:
math
math.PR

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)