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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2212.03841 |
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| _version_ | 1866917793999355904 |
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| author | Moradifam, Amir Rowell, Alexander |
| author_facet | Moradifam, Amir Rowell, Alexander |
| contents | We study existence and structure of solutions to the Dirichlet and Neumann boundary problems associated with minimizers of the functional $I(u)=\int_Ω (ϕ(x, D u + F)+Hu) \, dx$, where $ϕ(x, ξ)$, among other properties, is convex and homogeneous of degree $1$ with respect to $ξ$. We show that there exists an underlying vector field $N$ that characterizes the existence and structure of all minimizers. We also investigate existence of solutions under the barrier condition on $\partial Ω$. The results in this paper generalize and unify many results in the literature about existence of minimizers of least gradient problems and $P-$area minimizing surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_03841 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Existence and structure of solutions for general $P$-area minimizing surface Moradifam, Amir Rowell, Alexander Analysis of PDEs We study existence and structure of solutions to the Dirichlet and Neumann boundary problems associated with minimizers of the functional $I(u)=\int_Ω (ϕ(x, D u + F)+Hu) \, dx$, where $ϕ(x, ξ)$, among other properties, is convex and homogeneous of degree $1$ with respect to $ξ$. We show that there exists an underlying vector field $N$ that characterizes the existence and structure of all minimizers. We also investigate existence of solutions under the barrier condition on $\partial Ω$. The results in this paper generalize and unify many results in the literature about existence of minimizers of least gradient problems and $P-$area minimizing surfaces. |
| title | Existence and structure of solutions for general $P$-area minimizing surface |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2212.03841 |