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arXiv · 2508.01094

Differential Inclusions for Gradient and Symmetrized Gradient Operators

Nurun Nesha
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Abstract

In this article, we study the necessary and sufficient conditions for the existence of solutions in $W_0^{1,\infty}(\Omega;\mathbb R^n)$ in the minimal dimension of $\textrm{span }E$ for the following problem: \begin{equation*} P(D)u\in E \textrm{ a.e. in }\Omega, \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.

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Nurun Nesha. 2025-08-01. Differential Inclusions for Gradient and Symmetrized Gradient Operators. https://arxiv.org/abs/2508.01094

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