clopen.solutions

Open problems

980 registered problems.

OP-00286 Open
A fractal Weyl lower bound for obstacle resonances
SP · AIM Open Applied Problems · fractal Weyl laws · obstacle scattering · scattering resonances
OP-00347 Open
Full-order resonance growth for every nonzero real compact potential
SP · AIM Open Applied Problems · scattering resonances · Schrödinger operators
OP-00356 Open
Jakobson–Naud’s essential spectral-gap conjecture
SP · AIM Open Applied Problems · hyperbolic surfaces · scattering resonances · spectral gaps
OP-00363 Open
Infinitely many obstacle resonances in a fixed strip under trapping
AP · AIM Open Applied Problems · billiards · obstacle scattering · scattering resonances
OP-00442 Open
Global L2 scattering for the planar hyperbolic cubic Schrödinger equation
AP · AIM Open Applied Problems · dispersive equations · nonlinear Schrödinger equations · scattering
OP-00443 Open
A resonance gap for arbitrary uniformly hyperbolic trapping in three dimensions
SP · AIM Open Applied Problems · hyperbolic trapped sets · scattering resonances · semiclassical analysis
OP-00521 Open
Recover an arbitrary sound speed from one incident direction
AP · AIM Open Applied Problems · fixed angle scattering · inverse scattering · sound speeds
OP-00530 Open
Global uniqueness from inverse backscattering data
AP · AIM Open Applied Problems · backscattering data · inverse scattering · Schrödinger operators
OP-00541 Open
Lens rigidity for nontrapping surfaces with conjugate points
DG · AIM Open Applied Problems · conjugate points · lens rigidity · scattering relations
OP-00559 Open
Determine a smooth sound-soft obstacle from one far-field pattern
AP · AIM Open Applied Problems · far-field patterns · Helmholtz equation · inverse obstacle scattering
OP-00656 Open
Scattering of arbitrary small energy data for the three-dimensional Zakharov system
AP · AIM Open Applied Problems · dispersive equations · scattering · Zakharov system
OP-00767 Solution claimed
Characterizing realizable geodesic scattering data
DG · AIM Open Applied Problems · geometric inverse problems · scattering relation · simple surfaces