Publication Cover
Applicable Analysis
An International Journal
Volume 4, 1974 - Issue 1
18
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Integral operators for elliptic equations in three independent variables

Pages 77-95 | Published online: 02 May 2007

References

  • Bergman , S. 1953 . Integral Operators in the Theory of Linear partial Differential Equations in Mathematical physics , New York : Academic Press .
  • Bergman , S. and Schiffer , M. 1953 . Kernel Funciton and Elliptic Differntial Equation in Mathamatical physics , New York : Academic press .
  • Browder , F.E. 1962 . Approximation by solutions of partial differential equations . Amer J.Math , 84 : 134 – 160 .
  • Colton , D. 1971 . On the inverse scattering problem for axially symmetric solutions of the Helmholtz equation . Quart.J.Math , 22 : 288 – 294 .
  • Colton , D. and Gilbert , R.P. 1971 . New results on the approximation of solutions to partial differential equations the method of particular solutions in . Analytic Theory of Differential Equations , 183 : 207 – 212 .
  • Colton , D. and Gilbert , R.P. 1971 . An integral operator approach to Cauchy's problem for △p+2X+F(X)u(x)=0 . SIAM J.Math.Anal , 2 : 113 – 132 .
  • Friedlander , F.G. 1967 . On an improperly posed characteristic initial value problem . J Math.Mech , 16 : 907 – 915 .
  • Fuks , B.A. 1965 . Special Chapters in the Theory of Analytic Funcitons of Several Complex Variable , American Mathematical Society .
  • Garabedian , P.R. 1964 . ;Partial Differential Equations , New York : John wiley .
  • Gilbert , R.P. 1969 . Funciton Theoretic Methods in Partical Differential Equations , New York : Academic Press .
  • Gilbert , R.P. 1970 . The construciton of solutions for boundary value problems by function theoretic methods . SIAM J Math.Anal , 1 : 96 – 114 .
  • Gilbert , R.P. and Howard , H.C. 1967 . On a class of elliptic partial differential equations . Port.Math. , 26 : 353 – 373 .
  • Gilbert , R.P. and Lo , C.Y. 1971 . On the approximation of solutions of elliptic partial differential equations in two and three dimensions . SIAM J Math.Anal , 2 : 17 – 30 .
  • Henrici , P. 1957 . A survey of I.N.Vekua's theory of elliptic partial differential equations with analytic coefficients . Z Angew.Math.phys , 8 : 169 – 203 .
  • Henrici , P. 1960 . Completer systmes of solutions for a class of singular elliptic partial differential equations in , Madison : University of wisconsin press .
  • Hormander , L. 1964 . Linear Partial Differential Operators , Berlin : Springer-Verlag .
  • Lax , P.D. 1956 . A stability theory of abstract differential equations and its application to the study of local behaviors of solutions of elliptic equations . Comm.Pure App.Math. , 9 : 747 – 766 .
  • Malgrange , B. 1956 . Existence et approximation des solutions des equations aux derivees partielles et des equations de convolutions . Ann.Inst.Fourier , 6 : 271 – 355 .
  • Tjong , B.L. 1968 . Operators generating solutions of certain partial differential equations and their properties dissertation , kentucky : University of Kentucky .
  • Tjong , B.L. 1970 . Operators generating solutions of △ (x,y,z)+F(x,y,z)ScZ .nasymp;(x,y,z)=0 and their properties in . Analytic Methods in Mathematical Physics ,
  • Vekua , I.N. 1967 . New Methods for Solving Elliptic Equations , New York : John Wiley .

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.