Nonlinear Young differential equations: a review
Lucio Galeati

TL;DR
This paper reviews the theory of nonlinear Young differential equations, highlighting well-posedness, numerical schemes, and PDEs, with extensions to infinite-dimensional spaces and minimal assumptions.
Contribution
It provides a comprehensive, self-contained account of nonlinear Young equations, including new results on convergence and PDEs in Banach spaces.
Findings
Well-posedness results for nonlinear Young differential equations
Convergence analysis of numerical schemes
Extension to nonlinear Young PDEs in Banach spaces
Abstract
Nonlinear Young integrals have been first introduced in [Catellier,Gubinelli, SPA 2016] and provide a natural generalisation of classical Young ones, but also a versatile tool in the pathwise study of regularisation by noise phenomena. We present here a self-contained account of the theory, focusing on wellposedness results for abstract nonlinear Young differential equations, together with some new extensions; convergence of numerical schemes and nonlinear Young PDEs are also treated. Most results are presented for general (possibly infinite dimensional) Banach spaces and without using compactness assumptions, unless explicitly stated.
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