Non-symmetric Lévy-type operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909168102801408 |
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| author | Minecki, Jakub Szczypkowski, Karol |
| author_facet | Minecki, Jakub Szczypkowski, Karol |
| contents | We present a general approach to the parametrix construction. We apply it to prove the uniqueness and existence of a weak fundamental solution for the equation $\partial_t =\mathcal{L}$ with non-symmetric non-local operators $$ \mathcal{L}f(x):= b(x)\cdot \nabla f(x)+ \int_{\mathbb{R}^d}( f(x+z)-f(x)- 1_{|z|<1} \left<z,\nabla f(x)\right>)κ(x,z)J(z)\, dz\,, $$ under certain assumptions on $b$, $κ$ and $J$. The result allows more general coefficients even for $J(z)=|z|^{-d-1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13101 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-symmetric Lévy-type operators Minecki, Jakub Szczypkowski, Karol Analysis of PDEs Primary 60J35, 47G20, Secondary 47D06, 47A55 We present a general approach to the parametrix construction. We apply it to prove the uniqueness and existence of a weak fundamental solution for the equation $\partial_t =\mathcal{L}$ with non-symmetric non-local operators $$ \mathcal{L}f(x):= b(x)\cdot \nabla f(x)+ \int_{\mathbb{R}^d}( f(x+z)-f(x)- 1_{|z|<1} \left<z,\nabla f(x)\right>)κ(x,z)J(z)\, dz\,, $$ under certain assumptions on $b$, $κ$ and $J$. The result allows more general coefficients even for $J(z)=|z|^{-d-1}$. |
| title | Non-symmetric Lévy-type operators |
| topic | Analysis of PDEs Primary 60J35, 47G20, Secondary 47D06, 47A55 |
| url | https://arxiv.org/abs/2112.13101 |