On approximation of convex functionals with a convexity constraint and general Lagrangians
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911205018304512 |
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| author | Kim, Young Ho |
| author_facet | Kim, Young Ho |
| contents | In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order equations of Abreu type. Our result generalizes that of Le (Twisted Harnack inequality and approximation of variational problems with a convexity constraint by singular Abreu equations. Adv. Math. 434 (2023)) where the case of quadratically growing Lagrangians was treated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On approximation of convex functionals with a convexity constraint and general Lagrangians Kim, Young Ho Analysis of PDEs In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order equations of Abreu type. Our result generalizes that of Le (Twisted Harnack inequality and approximation of variational problems with a convexity constraint by singular Abreu equations. Adv. Math. 434 (2023)) where the case of quadratically growing Lagrangians was treated. |
| title | On approximation of convex functionals with a convexity constraint and general Lagrangians |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.07783 |