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Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces

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Main Authors: Giulia, Cavagnari, Giuseppe, Savaré, Giacomo Enrico, Sodini
Format: Book
Language:English
Published: Springer 2023
Subjects:
Wasserstein space P2(X) of Borel probability
Hilbert space X
Online Access:https://link.springer.com/article/10.1007/s00440-022-01148-7
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7465
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spelling oai:localhost:PNK-74652023-04-04T02:04:35Z Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces Giulia, Cavagnari Giuseppe, Savaré Giacomo Enrico, Sodini Wasserstein space P2(X) of Borel probability Hilbert space X CC BY We introduce and investigate a notion of multivalued λ-dissipative probability vector field (MPVF) in the Wasserstein space P2(X) of Borel probability measures on a Hilbert space X. Taking inspiration from the theories of dissipative operators in Hilbert spaces and of Wasserstein gradient flows for geodesically convex functionals, we study local and global well posedness of evolution equations driven by dissipative MPVFs. Our approach is based on a measure-theoretic version of the Explicit Euler scheme, for which we prove novel convergence results with optimal error estimates under an abstract stability condition, which do not rely on compactness arguments and also hold when X has infinite dimension. 2023-04-04T02:04:35Z 2023-04-04T02:04:35Z 2022 Book https://link.springer.com/article/10.1007/s00440-022-01148-7 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7465 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic Wasserstein space P2(X) of Borel probability
Hilbert space X
spellingShingle Wasserstein space P2(X) of Borel probability
Hilbert space X
Giulia, Cavagnari
Giuseppe, Savaré
Giacomo Enrico, Sodini
Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces
description CC BY
format Book
author Giulia, Cavagnari
Giuseppe, Savaré
Giacomo Enrico, Sodini
author_facet Giulia, Cavagnari
Giuseppe, Savaré
Giacomo Enrico, Sodini
author_sort Giulia, Cavagnari
title Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces
title_short Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces
title_full Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces
title_fullStr Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces
title_full_unstemmed Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces
title_sort dissipative probability vector fields and generation of evolution semigroups in wasserstein spaces
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00440-022-01148-7
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7465
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score 8.891787

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