Log-type ultra-analyticity of elliptic equations with gradient terms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929496423137280 |
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| author | Dong, Hongjie Wang, Ming |
| author_facet | Dong, Hongjie Wang, Ming |
| contents | It is well known that every solution of an elliptic equation is analytic if its coefficients are analytic. However, less is known about the ultra-analyticity of such solutions. This work addresses the problem of elliptic equations with lower-order terms, where the coefficients are entire functions of exponential type. We prove that every solution satisfies a quantitative logarithmic ultra-analytic bound and demonstrate that this bound is sharp. The results suggest that the ultra-analyticity of solutions to elliptic equations cannot be expected to achieve the same level of ultra-analyticity as the coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log-type ultra-analyticity of elliptic equations with gradient terms Dong, Hongjie Wang, Ming Analysis of PDEs 35J15, 26E05, 35A20 It is well known that every solution of an elliptic equation is analytic if its coefficients are analytic. However, less is known about the ultra-analyticity of such solutions. This work addresses the problem of elliptic equations with lower-order terms, where the coefficients are entire functions of exponential type. We prove that every solution satisfies a quantitative logarithmic ultra-analytic bound and demonstrate that this bound is sharp. The results suggest that the ultra-analyticity of solutions to elliptic equations cannot be expected to achieve the same level of ultra-analyticity as the coefficients. |
| title | Log-type ultra-analyticity of elliptic equations with gradient terms |
| topic | Analysis of PDEs 35J15, 26E05, 35A20 |
| url | https://arxiv.org/abs/2409.07027 |