Equivalence between Superharmonic functions and renormalized solutions for the equations with $(p, q)$-growth
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916693021818880 |
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| author | Li, Ying Zhang, Chao |
| author_facet | Li, Ying Zhang, Chao |
| contents | We establish the equivalence between superharmonic functions and locally renormalized solutions for the elliptic measure data problems with $(p, q)$-growth. By showing that locally renormalized solutions are essentially bounded below and using Wolff potential estimates, we extend the results of [T. Kilpeläinen, T. Kuusi, A. Tuhola-Kujanpää, Superharmonic functions are locally renormalized solutions, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 2011] to a broader class of problems. Our work provides the first equivalence result between locally renormalized solutions and superharmonic functions for the nonstandard growth equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11719 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalence between Superharmonic functions and renormalized solutions for the equations with $(p, q)$-growth Li, Ying Zhang, Chao Analysis of PDEs We establish the equivalence between superharmonic functions and locally renormalized solutions for the elliptic measure data problems with $(p, q)$-growth. By showing that locally renormalized solutions are essentially bounded below and using Wolff potential estimates, we extend the results of [T. Kilpeläinen, T. Kuusi, A. Tuhola-Kujanpää, Superharmonic functions are locally renormalized solutions, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 2011] to a broader class of problems. Our work provides the first equivalence result between locally renormalized solutions and superharmonic functions for the nonstandard growth equations. |
| title | Equivalence between Superharmonic functions and renormalized solutions for the equations with $(p, q)$-growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.11719 |