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A solution theory for quasilinear singular SPDEs

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Title: A solution theory for quasilinear singular SPDEs
Authors: Gerencsér, M
Hairer, M
Item Type: Journal Article
Abstract: We give a construction allowing us to build local renormalized solutions to general quasilinear stochastic PDEs within the theory of regularity structures, thus greatly generalizing the recent results of [1, 5, 11]. Loosely speaking, our construction covers quasilinear variants of all classes of equations for which the general construction of [3, 4, 7] applies, including in particular one‐dimensional systems with KPZ‐type nonlinearities driven by space‐time white noise. In a less singular and more specific case, we furthermore show that the counterterms introduced by the renormalization procedure are given by local functionals of the solution. The main feature of our construction is that it allows exploitation of a number of existing results developed for the semilinear case, so that the number of additional arguments it requires is relatively small.
Issue Date: Sep-2019
Date of Acceptance: 15-Feb-2018
URI: http://hdl.handle.net/10044/1/57175
DOI: https://doi.org/10.1002/cpa.21816
ISSN: 0010-3640
Publisher: Wiley
Start Page: 1983
End Page: 2005
Journal / Book Title: Communications on Pure and Applied Mathematics
Volume: 72
Issue: 9
Copyright Statement: © 2018 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
math.AP
math.AP
math.PR
math.AP
math.AP
math.PR
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Notes: 20 pages
Publication Status: Published
Online Publication Date: 2019-02-08
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics