On $L$-special domains with algebraic boundaries
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913819211595776 |
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| author | Borovikov, Mikhail |
| author_facet | Borovikov, Mikhail |
| contents | The concept of $L$-special domain appeared in the early 2000s. This analytical characteristic of domains in the complex plane is related to the problem on uniform approximation of functions on Carathéodory compacts in $\mathbb{R}^2$ by polynomial solutions of homogeneous second-order elliptic partial differential equations $Lu=0$ with constant complex coefficients. In this paper, new properties and examples of $L$-special domains with algebraic boundaries are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $L$-special domains with algebraic boundaries Borovikov, Mikhail Complex Variables Analysis of PDEs The concept of $L$-special domain appeared in the early 2000s. This analytical characteristic of domains in the complex plane is related to the problem on uniform approximation of functions on Carathéodory compacts in $\mathbb{R}^2$ by polynomial solutions of homogeneous second-order elliptic partial differential equations $Lu=0$ with constant complex coefficients. In this paper, new properties and examples of $L$-special domains with algebraic boundaries are obtained. |
| title | On $L$-special domains with algebraic boundaries |
| topic | Complex Variables Analysis of PDEs |
| url | https://arxiv.org/abs/2505.01765 |