Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s00440-022-01148-7 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7465 |
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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 |
| _version_ |
1762274897076158464 |
| score |
8.881002 |