Publication Cover
Applicable Analysis
An International Journal
Volume 45, 1992 - Issue 1-4
34
Views
24
CrossRef citations to date
0
Altmetric
Original Articles

The Invertibility of the Double Layer Potential Operator in the Space of Continuous Functions Defined on a Polyhedron: The Panel Method

Pages 135-177 | Published online: 02 May 2007

References

  • Angell , T.S. , Kleinman , R.E and Krai , J . 1988 . Layer potentials on boundaries with corners and edges . Casopis pro pestvani matematiky , 113 ( 4 ) : 387 – 402 .
  • Fabes,E.: Layer potential methods for boundary value problems on Lipschitz domains. in Kral,J. , J.Lukes, I.Netuka and J.Vesely (eds.) :Potential theory. Surveys and problems. Proceedings,Prague 1987 , Lecture Notes in Mathematics 1344, Springer-Verlag , Berlin-Heidelberg- New York, (1988)
  • Grachev , N.V. and Mazya , V.G. 1986 . On the Fredholm radius for operators of the double layer type over piece-wise smooth boundaries . Vestn. Leningr. Un.Mat.Mekh , 19 ( 4 ) : 60 – 64 .
  • Grachev , N.V. and Mazya , V.G. 1988 . Representation and estimates for the inverse operator of integral equations in potential theory for boundary surfaces with conical point . Soobch.A.N.GSSR , 132 ( 1 ) in russian
  • Jerison , D.S. and Kenig , C.E. 1981 . The Dirichlet problem in non-smooth domains . Annals of Mathematics , 113 ( 1 ) : 367 – 382 .
  • Jerison , D.S. and Kenig , C.E. 1981 . The Neumann problem in Lipschitz domains . Bulletin of AMS , 4 ( 1 ) : 203 – 207 .
  • Kral,J. : Integral operators in potential theory. Lecture Notes in Mathematics 823 , Springer-Verlag Berlin-Heidelberg-New York, (1980)
  • Kral , J. and Wendland , W. 1988 . “ On the applicability of the Fredholm-Radon method in potential theory and the panel method. in: Panel methods in fluid mechanics with emphasis in aero-dynamics ” . In Notes on Numerical Fluid Mechanics , Edited by: Ballmann , J. , Eppler , R. and Hackbusch , W. Vol. 21 , 120 – 136 . Vieweg .
  • Kral , J. and Wendland , W.L. 1986 . Some examples concerning applicability of the Fredholm-Radon method in potential theory . Aplikace matematky , 31 : 293 – 308 .
  • Mazya , V.G . 1988 . “ Boundary integral equations in Modern problems of mathematics ” . In Fundamental directions , Moscow, , Russian : Viniti .
  • Mc Lean , W. 1985 . Boundary integral methods for the Laplace equation . Thesis,Australian National University ,
  • Prö bdorf , S . 1978 . Some classes of singular equations , New York,Oxford : North-Holland Publ.Comp.Amsterdam .
  • Prö bdorf , S and Rathsfeld , A. 1984 . A spline collocation method for singular integral equations with piecewise continuous coefficients . Int.Equ.Op.Theory , 7 : 537 – 560 .
  • Rempel , S. 1989 . Corner singularity for transmission problems in three dimensions . Int,Equ. Op.Theory , 12 ( 6 ) : 835 – 854 .
  • Rempel , S. and Schmidt , G. 1991 . Eigenvalues for spherical domains with corners via boundary integral equations . Int.Equ.Op.Theory , 14 ( 6 ) : 229 – 250 .
  • Verchota , G.C. 1984 . Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains . Journal of Functional Analysis , 59 ( 6 ) : 572 – 611 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.