Rarity of $\boldsymbol{\mathcal{C}^{1,1}}$ solutions to the complex Monge--Ampère equation on weakly pseudoconvex domains
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913013436514304 |
|---|---|
| author | Bharali, Gautam Masanta, Rumpa |
| author_facet | Bharali, Gautam Masanta, Rumpa |
| contents | We show that on any weakly pseudoconvex $B$-regular domain, the classical Dirichlet problem for the complex Monge--Ampère equation with $\mathcal{C}^\infty$-smooth data does not in general admit $\mathcal{C}^{1,1}$-smooth solutions. This working draft is a prelude to potential-theoretic solutions to some extension problems for mappings that were thought to rely on such $\mathcal{C}^{1,1}$-smooth solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rarity of $\boldsymbol{\mathcal{C}^{1,1}}$ solutions to the complex Monge--Ampère equation on weakly pseudoconvex domains Bharali, Gautam Masanta, Rumpa Complex Variables Analysis of PDEs 32T27, 32U05 (Primary) 32T40 (Secondary) We show that on any weakly pseudoconvex $B$-regular domain, the classical Dirichlet problem for the complex Monge--Ampère equation with $\mathcal{C}^\infty$-smooth data does not in general admit $\mathcal{C}^{1,1}$-smooth solutions. This working draft is a prelude to potential-theoretic solutions to some extension problems for mappings that were thought to rely on such $\mathcal{C}^{1,1}$-smooth solutions. |
| title | Rarity of $\boldsymbol{\mathcal{C}^{1,1}}$ solutions to the complex Monge--Ampère equation on weakly pseudoconvex domains |
| topic | Complex Variables Analysis of PDEs 32T27, 32U05 (Primary) 32T40 (Secondary) |
| url | https://arxiv.org/abs/2604.06437 |