Gradient estimates for degenerate elliptic measure data problems with double phase
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918480536666112 |
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| author | Song, Kyeong Youn, Yeonghun |
| author_facet | Song, Kyeong Youn, Yeonghun |
| contents | We study nonlinear elliptic equations modeled on \[ -\mathrm{div}\,(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du) = μ, \] where $2\le p<q<\infty$, $a(\cdot) \ge 0$, and $μ$ is a signed Borel measure with finite total mass. We prove local Calderón--Zygmund type gradient estimates for SOLA (Solutions Obtained as Limits of Approximations) by finding new and natural assumptions on $p$, $q$ and $a(\cdot)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gradient estimates for degenerate elliptic measure data problems with double phase Song, Kyeong Youn, Yeonghun Analysis of PDEs 35B65, 35J70, 35R05, 35R06 We study nonlinear elliptic equations modeled on \[ -\mathrm{div}\,(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du) = μ, \] where $2\le p<q<\infty$, $a(\cdot) \ge 0$, and $μ$ is a signed Borel measure with finite total mass. We prove local Calderón--Zygmund type gradient estimates for SOLA (Solutions Obtained as Limits of Approximations) by finding new and natural assumptions on $p$, $q$ and $a(\cdot)$. |
| title | Gradient estimates for degenerate elliptic measure data problems with double phase |
| topic | Analysis of PDEs 35B65, 35J70, 35R05, 35R06 |
| url | https://arxiv.org/abs/2605.02470 |