抛物型spde解的Holder估计

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Theory of Probability and its Applications Pub Date : 2021-10-03 DOI:10.1137/S0040585X97979524

S. Kuksin, N. Nadirashvili, Andrey L. Piatnitski

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引用次数: 16

摘要

本文研究了在~${\bf R}^n$有界区域上具有加性噪声的二阶随机偏微分方程。我们假设噪声的系数是L^p -函数，其中~p足够大。我们几乎肯定地证明了解是H\ \老连续函数，并且证明了相应的H\ \老范数具有任意阶的有限动量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Holder Estimates for Solutions of Parabolic SPDEs

This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of~${\bf R}^n$. We suppose that the coefficients of the noise are $L^p$-functions with sufficiently large~p. We prove that the solutions are H\"older-continuous functions almost surely (a.s.)\ and that the respective H\"older norms have finite momenta of any order.

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来源期刊

Theory of Probability and its Applications 数学-统计学与概率论

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

6 months

期刊介绍： Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.