Differential Inclusions for Gradient and Symmetrized Gradient Operators
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911309983907840 |
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| author | Nesha, Nurun |
| author_facet | Nesha, Nurun |
| contents | In this article, we study the necessary and sufficient conditions for the existence of solutions in $W_0^{1,\infty}(Ω;\mathbb R^n)$ in the minimal dimension of $\textrm{span }E$ for the following problem: \begin{equation*} P(D)u\in E \textrm{ a.e. in }Ω, \end{equation*} where $P(D)= D$ or $D+D^{\top}$, and $E\subseteq \mathbb R^{n\times n}$ is a given set. We conclude this paper with some properties of real symmetric matrices. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_01094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differential Inclusions for Gradient and Symmetrized Gradient Operators Nesha, Nurun Analysis of PDEs In this article, we study the necessary and sufficient conditions for the existence of solutions in $W_0^{1,\infty}(Ω;\mathbb R^n)$ in the minimal dimension of $\textrm{span }E$ for the following problem: \begin{equation*} P(D)u\in E \textrm{ a.e. in }Ω, \end{equation*} where $P(D)= D$ or $D+D^{\top}$, and $E\subseteq \mathbb R^{n\times n}$ is a given set. We conclude this paper with some properties of real symmetric matrices. |
| title | Differential Inclusions for Gradient and Symmetrized Gradient Operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.01094 |