Higher integrability for parabolic PDEs with generalized Orlicz growth
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912727532830720 |
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| author | Hästö, Peter Ok, Jihoon |
| author_facet | Hästö, Peter Ok, Jihoon |
| contents | We prove higher integrability of the gradient of weak solutions to nonlinear parabolic systems whose prototype is \[ \partial_t u-\mathrm{div}\Big(\frac{φ'(z, |\nabla u|)}{|\nabla u|}\nabla u\Big) =0, \qquad u=(u^1,\dots,u^N), \] where $φ$ is a generalized Young function. Special cases of our main theorem include previously known results for the $p$-growth, the variable exponent and the double phase growth. Also included are previously unknown borderline double phase growth and perturbed variable exponent growth, among others. The problem is controlled by a natural requirement of comparison of $φ$ between points in intrinsic parabolic cylinders via an (A1)-condition, which unifies disparate conditions from the special cases. Moreover, we handle both the singular and degenerate cases at the same time, providing a simple proof of a reverse Hölder type inequality, which is new even in the $p$-growth case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher integrability for parabolic PDEs with generalized Orlicz growth Hästö, Peter Ok, Jihoon Analysis of PDEs 35K92, 35B65, 46E30 We prove higher integrability of the gradient of weak solutions to nonlinear parabolic systems whose prototype is \[ \partial_t u-\mathrm{div}\Big(\frac{φ'(z, |\nabla u|)}{|\nabla u|}\nabla u\Big) =0, \qquad u=(u^1,\dots,u^N), \] where $φ$ is a generalized Young function. Special cases of our main theorem include previously known results for the $p$-growth, the variable exponent and the double phase growth. Also included are previously unknown borderline double phase growth and perturbed variable exponent growth, among others. The problem is controlled by a natural requirement of comparison of $φ$ between points in intrinsic parabolic cylinders via an (A1)-condition, which unifies disparate conditions from the special cases. Moreover, we handle both the singular and degenerate cases at the same time, providing a simple proof of a reverse Hölder type inequality, which is new even in the $p$-growth case. |
| title | Higher integrability for parabolic PDEs with generalized Orlicz growth |
| topic | Analysis of PDEs 35K92, 35B65, 46E30 |
| url | https://arxiv.org/abs/2511.19758 |