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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18979 |
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| _version_ | 1866909933021167616 |
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| author | Giannone, Gabriele |
| author_facet | Giannone, Gabriele |
| contents | We establish sufficient conditions for the local boundedness of weak solutions to a broad class of nonlinear elliptic equations in divergence form, under unbalanced growth conditions on the stress field. Our analysis is carried out in a non-variational setting, with no symmetry or structural assumptions on the operator. The ellipticity and growth are prescribed via distinct Young functions, leading to a Orlicz-type setting that captures a wide class of nonstandard behaviors. As a special case, the theory encompasses and extends the known results on equations with $p,q$-growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local boundedness of weak solutions to elliptic equations under unbalanced Orlicz growth conditions Giannone, Gabriele Analysis of PDEs 35J60 (Primary) 46E30 (Secondary) We establish sufficient conditions for the local boundedness of weak solutions to a broad class of nonlinear elliptic equations in divergence form, under unbalanced growth conditions on the stress field. Our analysis is carried out in a non-variational setting, with no symmetry or structural assumptions on the operator. The ellipticity and growth are prescribed via distinct Young functions, leading to a Orlicz-type setting that captures a wide class of nonstandard behaviors. As a special case, the theory encompasses and extends the known results on equations with $p,q$-growth. |
| title | Local boundedness of weak solutions to elliptic equations under unbalanced Orlicz growth conditions |
| topic | Analysis of PDEs 35J60 (Primary) 46E30 (Secondary) |
| url | https://arxiv.org/abs/2510.18979 |