Interior a priori estimate for higher order elliptic systems in Orlicz spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916044781649920 |
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| author | Gogatishvili, Amiran Salerno, Pia Softova, Lubomira |
| author_facet | Gogatishvili, Amiran Salerno, Pia Softova, Lubomira |
| contents | We study singular integral operators with variable Calderón--Zygmund kernels and their commutators with $VMO$ functions in the framework of Orlicz spaces. After revisiting the classical $L^p$ theory, we establish boundedness results in $L^Φ$ under standard $Δ_2$ and $\nabla_2$ conditions on the Young function. The proofs rely on decomposition techniques and weak-type estimates. As an application, these results provide a functional-analytic foundation for a priori estimates and interior regularity of solutions to higher-order elliptic operators with discontinuous coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25780 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Interior a priori estimate for higher order elliptic systems in Orlicz spaces Gogatishvili, Amiran Salerno, Pia Softova, Lubomira Analysis of PDEs 30H35, 32A37, 35D35, 35J48, 35J58, 42B20, 42B25, 46E30, 46E35, 47G10 We study singular integral operators with variable Calderón--Zygmund kernels and their commutators with $VMO$ functions in the framework of Orlicz spaces. After revisiting the classical $L^p$ theory, we establish boundedness results in $L^Φ$ under standard $Δ_2$ and $\nabla_2$ conditions on the Young function. The proofs rely on decomposition techniques and weak-type estimates. As an application, these results provide a functional-analytic foundation for a priori estimates and interior regularity of solutions to higher-order elliptic operators with discontinuous coefficients. |
| title | Interior a priori estimate for higher order elliptic systems in Orlicz spaces |
| topic | Analysis of PDEs 30H35, 32A37, 35D35, 35J48, 35J58, 42B20, 42B25, 46E30, 46E35, 47G10 |
| url | https://arxiv.org/abs/2605.25780 |