$\mathcal{D}$-solutions to the system of vectorial Calculus of Variations in $L^โ$ via the singular value problem
$\mathcal{D}$-solutions to the system of vectorial Calculus of Variations in $L^โ$ via the singular value problem
For $\mathrm{H}โ C^2(\mathbb{R}^{N\times n})$ and $u :ฮฉ \subseteq \mathbb{R}^n \longrightarrow \mathbb{R}^N$ , consider the system$ \label{1}\mathrm{A}_โ u\, :=\,\Big(\mathrm{H}_P \otimes \mathrm{H}_P + \mathrm{H}[\mathrm{H}_P]^\bot \mathrm{H}_{PP}\Big)(\text{D} u):\text{D}^2u\, =\,0. \tag{1}$We construct $\mathcal{D}$ -solutions to the Dirichlet problem for (1), an apt notion of generalised solutions recently proposed for fully nonlinear systems. Our $\mathcal{D}$ -solutions โฆ