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Project A2: Singular integral operators and stochastic processes


Principal Investigator(s)
Moritz Kaßmann

Summary:

We develop a mathematical theory for nonlocal and discrete differential operators, which are related to Markov processes on subsets of the Euclidean space or graphs. We focus on results which are crucial for an understanding of the underlying dynamics independent of regularity assumptions on the state space or inhomogeneities of the medium. In this project, we study the following two interrelated parts, which go beyond current research and provide several new mathematical challenges: (I) Nonlocal operators with logarithmic order of differentiability and (II) Nonlocal operators and Markov processes on graphs.


Recent Preprints:

18078 Grzegorz Karch, Moritz Kaßmann, Milosz Krupski PDF

A framework for non-local, non-linear initial value problems

Project: A2

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A framework for non-local, non-linear initial value problems


Authors: Grzegorz Karch, Moritz Kaßmann, Milosz Krupski Projects: A2
Submission Date: 23.12.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18078

18077 Jamil Chaker, Moritz Kaßmann PDF

Nonlocal operators with singular anisotropic kernels

Project: A2

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Nonlocal operators with singular anisotropic kernels


Authors: Jamil Chaker, Moritz Kaßmann Projects: A2
Submission Date: 23.12.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18077

18076 Moritz Kaßmann, Vanja Wagner PDF

Nonlocal quadratic forms with visibility constraint

Project: A2

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Nonlocal quadratic forms with visibility constraint


Authors: Moritz Kaßmann, Vanja Wagner Projects: A2
Submission Date: 23.12.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18076

18075 Moritz Kaßmann, Andrey Piatnitski, Elena Zhizhina PDF

Homogenization of Lévy-type operators with oscillating coefficients

Project: A2

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Homogenization of Lévy-type operators with oscillating coefficients


Authors: Moritz Kaßmann, Andrey Piatnitski, Elena Zhizhina Projects: A2
Submission Date: 23.12.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18075



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