On the analyticity of solutions to non-linear elliptic partial differential equations
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866914901173207040 |
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| author | Blatt, Simon |
| author_facet | Blatt, Simon |
| contents | We give an easy proof of the fact that $C^\infty$ solutions to non-linear elliptic equations of second order $$
ϕ(x, u, D u, D^2 u)=0 $$ are analytic. Following ideas of Kato, the proof uses an inductive estimate for suitable weighted derivatives. We then conclude the proof using Cauchy's method of majorants}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_08762 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the analyticity of solutions to non-linear elliptic partial differential equations Blatt, Simon Analysis of PDEs 35A20, 35B65 We give an easy proof of the fact that $C^\infty$ solutions to non-linear elliptic equations of second order $$ ϕ(x, u, D u, D^2 u)=0 $$ are analytic. Following ideas of Kato, the proof uses an inductive estimate for suitable weighted derivatives. We then conclude the proof using Cauchy's method of majorants}. |
| title | On the analyticity of solutions to non-linear elliptic partial differential equations |
| topic | Analysis of PDEs 35A20, 35B65 |
| url | https://arxiv.org/abs/2009.08762 |