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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.04909 |
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| _version_ | 1866915424374882304 |
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| author | Kogoj, Alessia E. Lima, Maria E. Viana, Arlúcio |
| author_facet | Kogoj, Alessia E. Lima, Maria E. Viana, Arlúcio |
| contents | In this work, we give sufficient conditions for the existence and uniqueness of the heat equation involving the operator
$$
Δ_{\mathcal{G}}=\dfrac{1}{2}\left(Δ_{x}+|x|^2Δ_{y}\right)
$$ in Marcinkiewicz spaces. Furthermore, we provide sufficient conditions for the existence of positive, symmetric, and self-similar solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Heat equation involving a Grushin operator in Marcinkiewcz spaces Kogoj, Alessia E. Lima, Maria E. Viana, Arlúcio Analysis of PDEs In this work, we give sufficient conditions for the existence and uniqueness of the heat equation involving the operator $$ Δ_{\mathcal{G}}=\dfrac{1}{2}\left(Δ_{x}+|x|^2Δ_{y}\right) $$ in Marcinkiewicz spaces. Furthermore, we provide sufficient conditions for the existence of positive, symmetric, and self-similar solutions. |
| title | On the Heat equation involving a Grushin operator in Marcinkiewcz spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.04909 |