Fractional one-sided measure theoretic second-order elliptic operators and applications to stochastic partial differential equations
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914179005284352 |
|---|---|
| author | Sousa, Kelvin J. R. |
| author_facet | Sousa, Kelvin J. R. |
| contents | In this work we introduce and study fractional measure theoretic elliptic operators on the torus and a new stochastic process named W-Brownian motion. We establish some regularity and spectral results related to the operators cited above, more precisely, we were able to provide sharp bounds for the growth rate of eigenvalues to an associated eigenvalue problem. Moreover, we show how the Cameron-Martin space associated to the W-Brownian motion relates to Sobolev spaces connected with the elliptic operators mentioned above. Finally applications of the theory developed on stochastic partial differential equations are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12866 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fractional one-sided measure theoretic second-order elliptic operators and applications to stochastic partial differential equations Sousa, Kelvin J. R. Analysis of PDEs Probability Spectral Theory In this work we introduce and study fractional measure theoretic elliptic operators on the torus and a new stochastic process named W-Brownian motion. We establish some regularity and spectral results related to the operators cited above, more precisely, we were able to provide sharp bounds for the growth rate of eigenvalues to an associated eigenvalue problem. Moreover, we show how the Cameron-Martin space associated to the W-Brownian motion relates to Sobolev spaces connected with the elliptic operators mentioned above. Finally applications of the theory developed on stochastic partial differential equations are given. |
| title | Fractional one-sided measure theoretic second-order elliptic operators and applications to stochastic partial differential equations |
| topic | Analysis of PDEs Probability Spectral Theory |
| url | https://arxiv.org/abs/2204.12866 |