Asymptotic average solutions for second order hypoelliptic PDEs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918001576509440 |
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| author | Kogoj, Alessia E. |
| author_facet | Kogoj, Alessia E. |
| contents | Following an analogous procedure with that used in \cite{kogoj_lanconelli_pizzetti}, in turn inspired by a 1909 paper by Pizzetti \cite{pizzetti}, we introduce the notion of {\it asymptotic average solutions} for hypoelliptic linear partial differential operators with non-negative characteristic form. This notion makes every Poisson equation $\elle u(x)=-f(x)$ with continuous data $f$ pointwise solvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic average solutions for second order hypoelliptic PDEs Kogoj, Alessia E. Analysis of PDEs 35K65, 35K70, 35H10, 35H20, 35D99, 35B05, 35D30 Following an analogous procedure with that used in \cite{kogoj_lanconelli_pizzetti}, in turn inspired by a 1909 paper by Pizzetti \cite{pizzetti}, we introduce the notion of {\it asymptotic average solutions} for hypoelliptic linear partial differential operators with non-negative characteristic form. This notion makes every Poisson equation $\elle u(x)=-f(x)$ with continuous data $f$ pointwise solvable. |
| title | Asymptotic average solutions for second order hypoelliptic PDEs |
| topic | Analysis of PDEs 35K65, 35K70, 35H10, 35H20, 35D99, 35B05, 35D30 |
| url | https://arxiv.org/abs/2504.19240 |