4 problems

Interior problem conjecture. There exists a function $f\in C_c^{\infty}(\overline D)$, not identically zero in $K$, such that $\mathcal R f(L)$ vanishes for every line $L$ that int…

Let $\Omega\subset\mathbb{R}^3$ be a compact domain, and let $\epsilon\in C^2(\mathcal{S}^2,\Omega)$ be an elastic strain field in an isotropic medium that satisfies equilibrium an…

Rubin's range characterization conjecture. A function $g\in C_c^\infty(\mathbb{S}^{n-1}\times(0,2))$ belongs to the range of the operator $f\mapsto\mathcal{M}f$ if and only if

Higher-order Compton scattering smoothing conjecture. For each scattering order $i$, $g_i$ is approximated by a Fourier integral operator $\mathcal{L}_i(\cdot,n_e)$ of order