5 problems

Triple-junction singularity conjecture. Along $4\Gamma_i$, the solution has a leading-order singularity of the form

Let $\gamma_0$ denote the portion of $\gamma$ lying in the strip $[-d/2,d/2) \times \mathbb{R}$ and define … These are the quasi-periodic Hilbert transform and Laplace double-layer…

Uniqueness conjecture. The corrected windowed boundary integral equation system $$ does not suffer from uniqueness issues.

Existence and uniqueness conjecture. The result holds for any $\varepsilon$.

The paper studies the gravity Helmholtz equation in an unbounded linearly stratified medium and defines radiation conditions intended to ensure uniqueness of the boundary value pro…