TY - JOUR

T1 - On the Properties of Quasi-periodic Boundary Integral Operators for the Helmholtz Equation

AU - Aylwin, Rubén

AU - Jerez-Hanckes, Carlos

AU - Pinto, José

N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020/4/1

Y1 - 2020/4/1

N2 - We study the mapping properties of boundary integral operators arising when solving two-dimensional, time-harmonic waves scattered by periodic domains. For domains assumed to be at least Lipschitz regular, we propose a novel explicit representation of Sobolev spaces for quasi-periodic functions that allows for an analysis analogous to that of Helmholtz scattering by bounded objects. Except for Rayleigh-Wood frequencies, continuity and coercivity results are derived to prove wellposedness of the associated first kind boundary integral equations.

AB - We study the mapping properties of boundary integral operators arising when solving two-dimensional, time-harmonic waves scattered by periodic domains. For domains assumed to be at least Lipschitz regular, we propose a novel explicit representation of Sobolev spaces for quasi-periodic functions that allows for an analysis analogous to that of Helmholtz scattering by bounded objects. Except for Rayleigh-Wood frequencies, continuity and coercivity results are derived to prove wellposedness of the associated first kind boundary integral equations.

KW - Boundary integral equations

KW - Gratings

KW - Quasi-periodic functions

KW - Wave scattering

UR - http://www.scopus.com/inward/record.url?scp=85082310475&partnerID=8YFLogxK

U2 - 10.1007/s00020-020-2572-9

DO - 10.1007/s00020-020-2572-9

M3 - Article

AN - SCOPUS:85082310475

SN - 0378-620X

VL - 92

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

M1 - 17

ER -