TY - JOUR
T1 - Lp -theory of boundary integral operators for domains with unbounded smooth boundary
AU - Rabinovich, Vladimir
N1 - Publisher Copyright:
© 2016 by De Gruyter.
PY - 2016
Y1 - 2016
N2 - The paper is devoted to the Lp-theory of boundary integral operators for boundary value problems described by anisotropic Helmholtz operators with variable coefficients in unbounded domains with unbounded smooth boundary. We prove the invertibility of boundary integral operators for Dirichlet and Neumann problems in the Bessel-potential spaces Hs,p(D), p ϵ (1, ∞), and the Besov spaces Bs p,q(D), p, q ϵ [1, ∞]. We prove also the Fredholmness of the Robin problem in these spaces and give the index formula.
AB - The paper is devoted to the Lp-theory of boundary integral operators for boundary value problems described by anisotropic Helmholtz operators with variable coefficients in unbounded domains with unbounded smooth boundary. We prove the invertibility of boundary integral operators for Dirichlet and Neumann problems in the Bessel-potential spaces Hs,p(D), p ϵ (1, ∞), and the Besov spaces Bs p,q(D), p, q ϵ [1, ∞]. We prove also the Fredholmness of the Robin problem in these spaces and give the index formula.
KW - Bessel-potential and Besov spaces
KW - Boundary integral operators
KW - unbounded boundary
UR - http://www.scopus.com/inward/record.url?scp=84995579017&partnerID=8YFLogxK
U2 - 10.1515/gmj-2016-0049
DO - 10.1515/gmj-2016-0049
M3 - Artículo
SN - 1072-947X
VL - 23
SP - 595
EP - 614
JO - Georgian Mathematical Journal
JF - Georgian Mathematical Journal
IS - 4
ER -