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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.10611 |
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| _version_ | 1866929315789144064 |
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| author | Addona, Davide Menegatti, Giorgio Miranda Jr, Michele |
| author_facet | Addona, Davide Menegatti, Giorgio Miranda Jr, Michele |
| contents | Given an abstract Wiener space $(X,γ,H)$, we consider an open set $O\subseteq X$ which satisfies certain smoothness and mean-curvature conditions. We prove that the rescaled resolvent operator associated to the Ornstein-Uhlenbeck operator with homogeneous Dirichlet boundary conditions on $O$ is gradient contractive in $L^p(X,γ)$ for every $p\in(1,\infty)$. This is the Gaussian counterpart of an analogous result for the rescaled resolvent operator associated to the Laplace operator $Δ$ in $L^p$ with respect to the Lebesgue measure, $p\in[1,\infty)$, with homogeneous Dirichlet boundary conditions on a bounded convex open set $O\subseteq \mathbb R^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient contractivity of a rescaled resolvent on domains in Wiener spaces Addona, Davide Menegatti, Giorgio Miranda Jr, Michele Analysis of PDEs Functional Analysis Probability Given an abstract Wiener space $(X,γ,H)$, we consider an open set $O\subseteq X$ which satisfies certain smoothness and mean-curvature conditions. We prove that the rescaled resolvent operator associated to the Ornstein-Uhlenbeck operator with homogeneous Dirichlet boundary conditions on $O$ is gradient contractive in $L^p(X,γ)$ for every $p\in(1,\infty)$. This is the Gaussian counterpart of an analogous result for the rescaled resolvent operator associated to the Laplace operator $Δ$ in $L^p$ with respect to the Lebesgue measure, $p\in[1,\infty)$, with homogeneous Dirichlet boundary conditions on a bounded convex open set $O\subseteq \mathbb R^n$. |
| title | Gradient contractivity of a rescaled resolvent on domains in Wiener spaces |
| topic | Analysis of PDEs Functional Analysis Probability |
| url | https://arxiv.org/abs/2404.10611 |