Journal article 1092 views 52 downloads
Regularity of stochastic nonlocal diffusion equations
Guangying Lv,
Hongjun Gao ,
Jinlong Wei ,
Jiang-lun Wu
arXiv
Swansea University Author: Jiang-lun Wu
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Abstract
In this paper, we are concerned with regularity of nonlocal stochastic partial differential equations of parabolic type. By using Companato estimates and Sobolev embedding theorem, we first show the H\"older continuity (locally in the whole state space $R^d$) for mild solutions of stochastic no...
| Published in: | arXiv |
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| Published: |
2018
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| Online Access: |
https://arxiv.org/abs/1801.04531 |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa39311 |
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2018-04-04T19:33:14Z |
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| last_indexed |
2020-07-03T18:58:40Z |
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cronfa39311 |
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SURis |
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2020-07-03T18:30:06.5555114 v2 39311 2018-04-04 Regularity of stochastic nonlocal diffusion equations dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2018-04-04 In this paper, we are concerned with regularity of nonlocal stochastic partial differential equations of parabolic type. By using Companato estimates and Sobolev embedding theorem, we first show the H\"older continuity (locally in the whole state space $R^d$) for mild solutions of stochastic nonlocal diffusion equations in the sense that the solutions u belong to the space $C_γ(DT;L^p(Ω))$ with the optimal Ho ̈lder continuity index $γ$ (which is given explicitly), where $D_T := [0,T] × D for T > 0$, and $D ⊂ R^d$ being a bounded domain. Then, by utilising tail estimates, we are able to obtain the estimates of mild solutions in $L^p(Ω; C_{γ^∗} (D_T ))$. What’s more, we give an explicit formula between the two index $γ$ and $γ^∗$. Moreover, we prove H ̈older continuity for mild solutions on bounded domains. Finally, we present a new criteria to justify H\"older continuity for the solutions on bounded domains. The novelty of this paper is that our method are suitable to the case of time-space white noise. Journal Article arXiv 12 2 2018 2018-02-12 https://arxiv.org/abs/1801.04531 COLLEGE NANME COLLEGE CODE Swansea University 2020-07-03T18:30:06.5555114 2018-04-04T15:55:36.0204349 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Guangying Lv 1 Hongjun Gao 2 Jinlong Wei 3 Jiang-lun Wu 4 39311__17637__a9fa824b3a414c2cb3ce3f3af9e2809d.pdf 39311.pdf 2020-07-03T18:27:22.7436252 Output 242256 application/pdf Author's Original true true eng |
| title |
Regularity of stochastic nonlocal diffusion equations |
| spellingShingle |
Regularity of stochastic nonlocal diffusion equations Jiang-lun Wu |
| title_short |
Regularity of stochastic nonlocal diffusion equations |
| title_full |
Regularity of stochastic nonlocal diffusion equations |
| title_fullStr |
Regularity of stochastic nonlocal diffusion equations |
| title_full_unstemmed |
Regularity of stochastic nonlocal diffusion equations |
| title_sort |
Regularity of stochastic nonlocal diffusion equations |
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dbd67e30d59b0f32592b15b5705af885 |
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dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu |
| author |
Jiang-lun Wu |
| author2 |
Guangying Lv Hongjun Gao Jinlong Wei Jiang-lun Wu |
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Journal article |
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arXiv |
| publishDate |
2018 |
| institution |
Swansea University |
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Faculty of Science and Engineering |
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|
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
| url |
https://arxiv.org/abs/1801.04531 |
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| description |
In this paper, we are concerned with regularity of nonlocal stochastic partial differential equations of parabolic type. By using Companato estimates and Sobolev embedding theorem, we first show the H\"older continuity (locally in the whole state space $R^d$) for mild solutions of stochastic nonlocal diffusion equations in the sense that the solutions u belong to the space $C_γ(DT;L^p(Ω))$ with the optimal Ho ̈lder continuity index $γ$ (which is given explicitly), where $D_T := [0,T] × D for T > 0$, and $D ⊂ R^d$ being a bounded domain. Then, by utilising tail estimates, we are able to obtain the estimates of mild solutions in $L^p(Ω; C_{γ^∗} (D_T ))$. What’s more, we give an explicit formula between the two index $γ$ and $γ^∗$. Moreover, we prove H ̈older continuity for mild solutions on bounded domains. Finally, we present a new criteria to justify H\"older continuity for the solutions on bounded domains. The novelty of this paper is that our method are suitable to the case of time-space white noise. |
| published_date |
2018-02-12T19:22:45Z |
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1821343970426355712 |
| score |
11.04748 |