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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.06054 |
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| _version_ | 1866912472169971712 |
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| author | Biagi, Stefano Cupini, Giovanni Mascolo, Elvira |
| author_facet | Biagi, Stefano Cupini, Giovanni Mascolo, Elvira |
| contents | We consider a class of {energy integrals}, associated to nonlinear and non-uniformly elliptic equations, with integrands $f(x,u,ξ)$ satisfying anisotropic $p_i,q$-growth conditions of the form $$ \sum_{i=1}^n λ_i (x)|ξ_i|^{p_i}\le {f}(x,u,ξ)\le μ(x)\left\{|ξ|^{q} + |u|^γ+1\right\} $$ for some exponents $γ\ge q\geq p_i>1$, and non-negative functions $λ_i,μ$ subject to suitable summability assumptions. We prove the local boundedness of scalar local quasi-minimizers of such integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local boundedness for solutions of a class of non-uniformly elliptic anisotropic problems Biagi, Stefano Cupini, Giovanni Mascolo, Elvira Analysis of PDEs We consider a class of {energy integrals}, associated to nonlinear and non-uniformly elliptic equations, with integrands $f(x,u,ξ)$ satisfying anisotropic $p_i,q$-growth conditions of the form $$ \sum_{i=1}^n λ_i (x)|ξ_i|^{p_i}\le {f}(x,u,ξ)\le μ(x)\left\{|ξ|^{q} + |u|^γ+1\right\} $$ for some exponents $γ\ge q\geq p_i>1$, and non-negative functions $λ_i,μ$ subject to suitable summability assumptions. We prove the local boundedness of scalar local quasi-minimizers of such integrals. |
| title | Local boundedness for solutions of a class of non-uniformly elliptic anisotropic problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.06054 |