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 -