Weak limit of homeomorphisms in $W^{1,n-1}$: invertibility and lower semicontinuity of energy
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918158812577792 |
|---|---|
| author | Doležalová, Anna Hencl, Stanislav Molchanova, Anastasia |
| author_facet | Doležalová, Anna Hencl, Stanislav Molchanova, Anastasia |
| contents | Let $Ω$, $Ω'\subset\mathbb{R}^n$ be bounded domains and let $f_m\colonΩ\toΩ'$ be a sequence of homeomorphisms with positive Jacobians $J_{f_m} >0$ a.e. and prescribed Dirichlet boundary data. Let all $f_m$ satisfy the Lusin (N) condition and $\sup_m \int_Ω(|Df_m|^{n-1}+A(|\text{cof} Df_m|)+ϕ(J_f))<\infty$, where $A$ and $φ$ are positive convex functions. Let $f$ be a weak limit of $f_m$ in $W^{1,n-1}$. Provided certain growth behaviour of $A$ and $φ$, we show that $f$ satisfies the (INV) condition of Conti and De Lellis, the Lusin (N) condition, and polyconvex energies are lower semicontinuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06452 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Weak limit of homeomorphisms in $W^{1,n-1}$: invertibility and lower semicontinuity of energy Doležalová, Anna Hencl, Stanislav Molchanova, Anastasia Functional Analysis Let $Ω$, $Ω'\subset\mathbb{R}^n$ be bounded domains and let $f_m\colonΩ\toΩ'$ be a sequence of homeomorphisms with positive Jacobians $J_{f_m} >0$ a.e. and prescribed Dirichlet boundary data. Let all $f_m$ satisfy the Lusin (N) condition and $\sup_m \int_Ω(|Df_m|^{n-1}+A(|\text{cof} Df_m|)+ϕ(J_f))<\infty$, where $A$ and $φ$ are positive convex functions. Let $f$ be a weak limit of $f_m$ in $W^{1,n-1}$. Provided certain growth behaviour of $A$ and $φ$, we show that $f$ satisfies the (INV) condition of Conti and De Lellis, the Lusin (N) condition, and polyconvex energies are lower semicontinuous. |
| title | Weak limit of homeomorphisms in $W^{1,n-1}$: invertibility and lower semicontinuity of energy |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2212.06452 |