Partial regularity for $\mathbb{A}$-quasiconvex functionals with Orlicz growth
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913167369568256 |
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| author | Stephan, Paul |
| author_facet | Stephan, Paul |
| contents | We establish partial regularity results for minimizers of a class of functionals depending on differential expressions based on elliptic operators. Specifically, we focus on functionals of Orlicz growth with a natural strong quasiconvexity property. In doing so, we consider both $Δ_{2}\cap\nabla_{2}$-Orlicz growth scenarios and, as a limiting case, $L \log L$-growth. Inspired by Conti & Gmeineder (J Calc Var, 61:215, 2022), the proofs of our main results are accomplished by reduction to the case of full gradient partial regularity results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial regularity for $\mathbb{A}$-quasiconvex functionals with Orlicz growth Stephan, Paul Analysis of PDEs We establish partial regularity results for minimizers of a class of functionals depending on differential expressions based on elliptic operators. Specifically, we focus on functionals of Orlicz growth with a natural strong quasiconvexity property. In doing so, we consider both $Δ_{2}\cap\nabla_{2}$-Orlicz growth scenarios and, as a limiting case, $L \log L$-growth. Inspired by Conti & Gmeineder (J Calc Var, 61:215, 2022), the proofs of our main results are accomplished by reduction to the case of full gradient partial regularity results. |
| title | Partial regularity for $\mathbb{A}$-quasiconvex functionals with Orlicz growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.09478 |