6533b828fe1ef96bd1288563

RESEARCH PRODUCT

Strictly convex corners scatter

Mikko SaloLassi PäivärintaEsa V. Vesalainen

subject

Plane (geometry)non-scattering energiesGeneral Mathematicsta111010102 general mathematicsMathematical analysis01 natural sciencescomplex geometrical optics solutions010101 applied mathematicsMathematics - Analysis of PDEscorner scatteringConic sectionFOS: MathematicsCountable set0101 mathematicsConvex functionMathematicsAnalysis of PDEs (math.AP)

description

We prove the absence of non-scattering energies for potentials in the plane having a corner of angle smaller than $\pi$. This extends the earlier result of Bl{\aa}sten, P\"aiv\"arinta and Sylvester who considered rectangular corners. In three dimensions, we prove a similar result for any potential with a circular conic corner whose opening angle is outside a countable subset of $(0,\pi)$.

yearjournalcountryeditionlanguage
2017-01-01
https://dx.doi.org/10.48550/arxiv.1404.2513