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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.02384 |
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| _version_ | 1866913609937846272 |
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| author | Chau, Albert Weinkove, Ben |
| author_facet | Chau, Albert Weinkove, Ben |
| contents | We consider the Dirichlet problem for a class of semilinear equations on two dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii.
We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02384 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Concavity of solutions to semilinear equations in dimension two Chau, Albert Weinkove, Ben Analysis of PDEs We consider the Dirichlet problem for a class of semilinear equations on two dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions. |
| title | Concavity of solutions to semilinear equations in dimension two |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2204.02384 |