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On the Rough Gronwall Lemma and Its Applications

  • Martina HofmanováEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)

Abstract

We present a rough path analog of the classical Gronwall Lemma introduced recently by Deya, Gubinelli, Hofmanová, Tindel in arXiv:1604.00437, [6] and discuss two of its applications. First, it is applied in the framework of rough path driven PDEs in order to establish energy estimates for weak solutions. Second, it is used in order to prove uniqueness for reflected rough differential equations.

Keywords

Rough paths Rough partial differential equations Reflected rough differential equations Rough gronwall lemma 

2010 Mathematics Subject Classification

60H15 35R60 35L65 

Notes

Acknowledgements

Financial support by the DFG via Research Unit FOR 2402 is gratefully acknowledged.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.Institute of MathematicsTechnical University BerlinBerlinGermany

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