Existence and uniqueness of weak solutions to quasilinear PDEs with critical data
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910183514439680 |
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| author | Bechtel, Sebastian Auscher, Pascal |
| author_facet | Bechtel, Sebastian Auscher, Pascal |
| contents | We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when the initial data is merely bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00439 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of weak solutions to quasilinear PDEs with critical data Bechtel, Sebastian Auscher, Pascal Analysis of PDEs Classical Analysis and ODEs Functional Analysis We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when the initial data is merely bounded. |
| title | Existence and uniqueness of weak solutions to quasilinear PDEs with critical data |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2605.00439 |