$H^\infty$-calculus for the Dirichlet Laplacian on conical domains
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912781521911808 |
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| author | Cioica-Licht, Petru A. Lorist, Emiel Werner, P. Tobias |
| author_facet | Cioica-Licht, Petru A. Lorist, Emiel Werner, P. Tobias |
| contents | We establish boundedness of the $H^\infty$-calculus for the Dirichlet Laplacian on conical domains in $\mathbb{R}^d$ and corresponding wedges on $L^p$-spaces with mixed weights. The weights are based on both the distance to the boundary and the distance to the tip/edge of the cone/wedge. Our main motivation comes from the study of stochastic partial differential equations and associated degenerate deterministic parabolic equations on non-smooth domains. As a consequence of our analysis, we also obtain maximal $L^p$-regularity for the Poisson equation on conical domains in appropriate weighted Sobolev spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $H^\infty$-calculus for the Dirichlet Laplacian on conical domains Cioica-Licht, Petru A. Lorist, Emiel Werner, P. Tobias Functional Analysis Analysis of PDEs Primary: 47A60, Secondary: 42B37, 46E35 We establish boundedness of the $H^\infty$-calculus for the Dirichlet Laplacian on conical domains in $\mathbb{R}^d$ and corresponding wedges on $L^p$-spaces with mixed weights. The weights are based on both the distance to the boundary and the distance to the tip/edge of the cone/wedge. Our main motivation comes from the study of stochastic partial differential equations and associated degenerate deterministic parabolic equations on non-smooth domains. As a consequence of our analysis, we also obtain maximal $L^p$-regularity for the Poisson equation on conical domains in appropriate weighted Sobolev spaces. |
| title | $H^\infty$-calculus for the Dirichlet Laplacian on conical domains |
| topic | Functional Analysis Analysis of PDEs Primary: 47A60, Secondary: 42B37, 46E35 |
| url | https://arxiv.org/abs/2509.09519 |