Nearness and solvability of non-invariant equations on stratified groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916289820229632 |
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| author | Chatzakou, Marianna Ruzhansky, Michael Yannakakis, Nikos |
| author_facet | Chatzakou, Marianna Ruzhansky, Michael Yannakakis, Nikos |
| contents | We prove the well-posedness of the differential equation $Au=f$ in the setting of a stratified group $\mathbb{G}$ when the considered second-order differential operator $A$ can be non-invariant and non-linear. Our approach follows the Campanato theory of nearness of operators, allowing one to treat equations with only bounded coefficients, without any regularity assumptions. Our analysis becomes explicit in the particular case of the Heisenberg group $\mathbb{H}^n$ of any dimension and on the Euclidean case $\mathbb{R}^n$, where in the latter case our results also extend the known results by treating the unbounded domain setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_11600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nearness and solvability of non-invariant equations on stratified groups Chatzakou, Marianna Ruzhansky, Michael Yannakakis, Nikos Analysis of PDEs Functional Analysis We prove the well-posedness of the differential equation $Au=f$ in the setting of a stratified group $\mathbb{G}$ when the considered second-order differential operator $A$ can be non-invariant and non-linear. Our approach follows the Campanato theory of nearness of operators, allowing one to treat equations with only bounded coefficients, without any regularity assumptions. Our analysis becomes explicit in the particular case of the Heisenberg group $\mathbb{H}^n$ of any dimension and on the Euclidean case $\mathbb{R}^n$, where in the latter case our results also extend the known results by treating the unbounded domain setting. |
| title | Nearness and solvability of non-invariant equations on stratified groups |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2406.11600 |