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Let $m: \mathcal{L}(\mathbb{R}^{d \times d}) \to \mathbb{R}$ be the function $$ m[H] = \frac{\lambda_{\max}(H[\mathbf{I}])}{\lambda_{\max}(H)}, $$ where $\lambda_{\max}$ denotes the largest eigenvalue....

In 1940 Sobolev recorded the following problem in the Scottish Book, and offered a bottle of wine for a solution. In 2015, when the second edition of the Scottish Book with updates and commentary on ...

I am reading the following paper of Struwe in which he proves the following result: Proposition 2.1: Let $n\geq 3$, $\lambda \in \mathbb{R}$ and $\Omega$ be a smoothly bounded domain in $\mathbb{R}^{n}...