The Neumann problem for the dissipative Helmholtz equation in the exterior of open Lipschitz surfaces

References

• McLean , W . 2000 . Strongly Elliptic Systems and Boundary Integral Equations , Cambridge : Cambridge University Press .
   Google Scholar
• Verchota , G . 1984 . Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains . J. Funct. Anal. , 59 : 572 – 611 .
   Google Scholar
• Jerison , D and Kenig , C . 1981 . The Neumann problem on Lipschitz domains . Bull. Amer. Math. Soc. , 4 : 203 – 207 .
   Google Scholar
• Grisvard , P . 1985 . Boundary Value Problems in Nonsmooth Domains , London : Pitman .
   Google Scholar
• Lifanov , IK , Poltavskii , LN and Vainikko , GM . 2004 . Hypersingular Integral Equations and Their Applications , Boca Raton : CRC Press .
   Google Scholar
• Povzner , AY and Sukharevskii , IV . 1960 . Integral equations of second kind in a problem of diffraction by an infinitely thin screen . Sov. Phys. Dokl. , 4 : 798 – 802 .
   Google Scholar
• Berkhin , PE . 1984 . Problem of diffraction of a fine screen . Siberian Math. J. , 25 : 31 – 42 .
   Google Scholar
• Sybil , Y . 1997 . Three-dimensional elliptic boundary value problems for an open Lipschitz surface . Matematychni Studii , 8 : 79 – 96 .
   Google Scholar
• Krutitskii , PA . 1998 . The Dirichlet problem for the dissipative Helmholtz equation in a plane domain bounded by closed and open curves . Hiroshima Math. J. , 28 ( 1 ) : 149 – 168 .
   Google Scholar
• Krutitskii , PA . 1999 . The Neumann problem in a plane domain bounded by closed and open curves . Complex Variables , 38 : 1 – 20 .
   Google Scholar
• Krutitskii , PA . 1997 . The 2-D Neumann problem in an exterior domain bounded by closed and open curves . Math. Methods Appl. Sci. , 20 ( 18 ) : 1551 – 1562 .
   Google Scholar
• Krutitskii , PA . 1999 . The 2-D Neumann problem in a domain with cuts . Rendiconti di Matematica (Roma), Ser. 7, , 19 : 65 – 88 .
   Google Scholar
• Krutitskii , PA . 2001 . The Neumann problem in a 2-D exterior domain with cuts and singularities at the tips . J. Differ. Eqns , 176 ( 1 ) : 269 – 289 .
   Google Scholar
• Krutitskii , PA . 1998 . The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves . Int. J. Math. Math. Sci. , 21 ( 2 ) : 209 – 216 . (Open access)
   Google Scholar
• Krutitskii , PA . 1997 . The Neumann problem for the 2-D Helmholtz equation in a multiply connected domain with cuts . Z. Anal. Anwend. , 16 ( 2 ) : 349 – 362 .
   Google Scholar
• Krutitskii , PA . 1998 . The Neumann problem on wave propagation in a 2-D external domain with cuts . J. Math. Kyoto Univ. , 38 ( 3 ) : 439 – 452 .
   Google Scholar
• Krutitskii , PA . 2000 . Acoustic scattering by several obstacles and screens with Neumann boundary condition . Math. Comput. simul. , 52 : 345 – 360 .
   Google Scholar
• Krutitskii , PA . 2000 . Wave scattering in a 2-D exterior domain with cuts: The Neumann problem . ZAMM , 80 ( 8 ) : 535 – 546 .
   Google Scholar