6 problems

Let $\Omega$ be a domain and let $u$ solve the semilinear Dirichlet problem … Here, $u$ is quasiconcave when its superlevel sets are convex. Lions' conjecture. For a general $f$, t…

Let $Z(\lambda)$ denote the marginal likelihood for a regularized linear regression model, with ridge, lasso, and group lasso corresponding to their respective regularizers. Quasic…

Iwaniec's conjecture. The critical power $B_K^{\alpha_{\max}}$ is $\operatorname{Curl}$-quasiconcave.

Zero-matrix quasiconcavity conjecture. Burkholder functions are quasiconcave at the zero matrix.

For $p\geqslant n/2$ and $\lambda\geqslant\left|1-n/p\right|$, define the Burkholder matrix function … The source also defines the planar Burkholder function…

For $n\geq 1$ and $p\geq n$, define the Burkholder functional … It is known that $\mathbf B_p^{\,n}$ is rank-one concave. Burkholder's higher-dimensional quasiconcavity conjecture.…