在变化设置中进行了推断结果:提高了规律性,紧性,以及对准线性系统的应用
Sebastian Bechtel1, Mark Veraar1
1Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.
概括
本研究将L^2估计扩展到变量设置中的随机局部微分方程 (SPDEs) 的L^p估计. 它还建立了一个通用紧性结果,证明了近线方程的弱解的全球存在.
科学领域:
- 随机分析 随机分析
- 部分微分方程 部分微分方程
- 功能分析是一种功能分析.
背景情况:
- 随机局部微分方程 (SPDEs) 对于建模复杂系统至关重要.
- 变量方法为分析SPDEs提供了一个强大的框架.
- 将经典L^2估计扩展到L^p估计是一个关键的挑战.
研究的目的:
- 在Gelfand三重设置中为SPDEs建立L^p估计.
- 为了获得SPDEs的通用紧性结果.
- 证明近线方程的弱解的全球存在.
主要方法:
- 使用Gelfand三重 (V,H,V*) 的框架.
- 在线性强制对 (A,B) 和对称性对 A. 的标准条件下,将 L^2 估计推算为 L^p 估计.
- 应用V对H的紧嵌入来得出紧性结果.
- 为全球存在证明利用紧性.
主要成果:
- 成功地将经典的L^2估计推断为SPDEs的L^p估计 (p > 2) 在 (A,B) 上没有额外条件的情况下.
- 获得解决方案路径的先验正则性结果.
- 推导出适用于所有 (A,B) 对的通用紧性结果,当V紧地嵌入H时.
- 证明了第二阶准线性方程系统的弱解的全球存在.
结论:
- 该研究为SPDEs的分析技术提供了显著的进步.
- 衍生出来的L^p估计和紧性结果提供了更广泛的适用性和对SPDE解决方案的更深入的理解.
- 这些发现对准线性部分微分方程存在理论有直接影响.
关键词:
强制性是一种强制性.紧性 紧性的额外推算是指进行额外推算.准线性和半线性的这就是Sneiberg的.随机进化方程 随机进化方程随机局部微分方程 随机局部微分方程紧张的 紧张的 紧张的变量方法 变量方法更多相关视频
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