奇异蜘蛛的全景图

Proceedings of the International Congress of Mathematicians (ICM 2018) Pub Date : 2019-05-01 DOI:10.1142/9789813272880_0140

M. Gubinelli

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引用次数: 12

摘要

我将回顾奇异随机偏微分方程(SSPDEs)领域的背景和一些最近的结果。自海尔发明规则结构以来，这一领域得到了迅速发展。SSPDEs是具有随机和不规则源项的非线性方程，这使得它在经典意义上是不适定的。他们的研究涉及随机分析、偏微分方程分析(包括准微分微积分)和代数之间的紧密相互作用。

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A PANORAMA OF SINGULAR SPDES

I will review the setting and some of the recent results in the field of singular stochastic partial differential equations (SSPDEs). Since Hairer’s invention of regularity structures this field has experienced a rapid development. SSPDEs are non-linear equations with random and irregular source terms which make them ill-posed in classical sense. Their study involves a tight interplay between stochastic analysis, analysis of PDEs (including paradifferential calculus) and algebra.

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Proceedings of the International Congress of Mathematicians (ICM 2018)

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