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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.14307 |
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| _version_ | 1866917009452695552 |
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| author | Uemura, Toshihiro Seesanea, Adisak |
| author_facet | Uemura, Toshihiro Seesanea, Adisak |
| contents | This work is concerned with homogenization problems for elliptic equations of the type \[ \begin{cases} \mathfrak{L}_δ u_δ + λu_δ = f_δ \qquad \text{in} \;\; D, \\ \qquad \quad \;\, u = 0 \qquad \, \text{on} \;\; \partial D, \end{cases} \] where $δ> 0$, $λ\in \mathbb{R}$, $D$ is a bounded open set in $\mathbb{R}^{d}$, and $f_δ \in H^{-1}(D)$. The operator $ \mathfrak{L}_δ u = -{\rm div} \left( A^δ\nabla u + C^δu \right) + B^δ\nabla u +k^δu $ involved uniformly bounded diffusion coefficients $A^δ$, where drifts $B^δ$, $C^δ$, and potential $k^δ$ are possibly unbounded. An application to homogenization of the corresponding diffusion processes is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14307 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homogenization of diffusion processes with singular drifts and potentials via unfolding method Uemura, Toshihiro Seesanea, Adisak Analysis of PDEs Probability 31C25 (Primary) 60J46, 35B27 (Secondary) This work is concerned with homogenization problems for elliptic equations of the type \[ \begin{cases} \mathfrak{L}_δ u_δ + λu_δ = f_δ \qquad \text{in} \;\; D, \\ \qquad \quad \;\, u = 0 \qquad \, \text{on} \;\; \partial D, \end{cases} \] where $δ> 0$, $λ\in \mathbb{R}$, $D$ is a bounded open set in $\mathbb{R}^{d}$, and $f_δ \in H^{-1}(D)$. The operator $ \mathfrak{L}_δ u = -{\rm div} \left( A^δ\nabla u + C^δu \right) + B^δ\nabla u +k^δu $ involved uniformly bounded diffusion coefficients $A^δ$, where drifts $B^δ$, $C^δ$, and potential $k^δ$ are possibly unbounded. An application to homogenization of the corresponding diffusion processes is also discussed. |
| title | Homogenization of diffusion processes with singular drifts and potentials via unfolding method |
| topic | Analysis of PDEs Probability 31C25 (Primary) 60J46, 35B27 (Secondary) |
| url | https://arxiv.org/abs/2306.14307 |