Partial regularity for degenerate systems of double phase type
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912076158468096 |
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| author | Ok, Jihoon Scilla, Giovanni Stroffolini, Bianca |
| author_facet | Ok, Jihoon Scilla, Giovanni Stroffolini, Bianca |
| contents | We study partial regularity for degenerate elliptic systems of double-phase type, where the growth function is given by $H(x,t)=t^p+a(x)t^q$ with $1<p\leq q$ and $a(x)$ a nonnegative $C^{0,α}$-continuous function. Our main result proves that if $\frac{q}{p}\leq 1+\fracα{n}$, the gradient of any weak solution is locally Hölder continuous, except on a set of measure zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial regularity for degenerate systems of double phase type Ok, Jihoon Scilla, Giovanni Stroffolini, Bianca Analysis of PDEs 35J47, 35J92, 35B65, 46E30 We study partial regularity for degenerate elliptic systems of double-phase type, where the growth function is given by $H(x,t)=t^p+a(x)t^q$ with $1<p\leq q$ and $a(x)$ a nonnegative $C^{0,α}$-continuous function. Our main result proves that if $\frac{q}{p}\leq 1+\fracα{n}$, the gradient of any weak solution is locally Hölder continuous, except on a set of measure zero. |
| title | Partial regularity for degenerate systems of double phase type |
| topic | Analysis of PDEs 35J47, 35J92, 35B65, 46E30 |
| url | https://arxiv.org/abs/2410.14350 |