The Construction of Solutions for Boundary Value Problems by Function Theoretic Methods

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Previous article Next article The Construction of Solutions for Boundary Value Problems by Function Theoretic MethodsR. P. GilbertR. P. Gilberthttps://doi.org/10.1137/0501010PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Stefan Bergman, Integral operators in the theory of linear partial differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Heft 23, Springer-Verlag, Berlin, 1961viii+145 MR0141880 0093.28701 CrossrefGoogle Scholar[2] Richard Courant and , David Hilbert, Methods of mathematical physics. Vol. II: Partial differential equations, (Vol. II by R. Courant.), Interscience Publishers (a division of John Wiley & Sons), New York-Lon don, 1962xxii+830 MR0140802 0099.29504 Google Scholar[3A] Arthur Erdélyi, Higher transcendental functions. Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xxvi+302 MR0058756 0051.30303 Google Scholar[3B] Arthur Erdélyi, Higher transcendental functions. Vol. II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xvii+396 MR0058756 0052.29502 Google Scholar[3C] Arthur Erdélyi, Higher transcendental functions. Vol. III, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955xvii+292 MR0066496 0064.06302 Google Scholar[4] Paul R. Garabedian, Partial differential equations, John Wiley & Sons Inc., New York, 1964xii+672 MR0162045 0124.30501 Google Scholar[5] Robert P. Gilbert, Function theoretic methods in partial differential equations, Mathematics in Science and Engineering, Vol. 54, Academic Press, New York, 1969xviii+311 MR0241789 0187.35303 Google Scholar[6] Robert P. Gilbert and , Henry C. Howard, On a class of elliptic partial differential equations, Portugal. Math., 26 (1967), 353–373 0195.11201 Google Scholar[7] Robert P. Gilbert and , Chi Yeung Lo, On the approximation of solutions of elliptic partial differential equations in two and three dimensions, SIAM J. Math. Anal., 2 (1971), 17–30 10.1137/0502002 MR0298212 0212.44802 LinkGoogle Scholar[8] Claus Müller, Spherical harmonics, Lecture Notes in Mathematics, Vol. 17, Springer-Verlag, Berlin, 1966iv+45 MR0199449 CrossrefGoogle Scholar[9] S. L. Sobolev and , E. R. Dawson, Partial differential equations of mathematical physics, Translated from the third Russian edition by E. R. Dawson; English translation edited by T. A. A. Broadbent, Pergamon Press, Oxford, 1964x+427 MR0178220 0123.06508 Google Scholar[10] Ilya N. Vekua, New methods for solving elliptic equations, Translated from the Russian by D. E. Brown. Translation edited by A. B. Tayler, North-Holland Publishing Co., Amsterdam, 1967xii+358 MR0212370 0146.34301 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Transmutation operators and complete systems of solutions for the radial Schrödinger equation17 March 2020 | Mathematical Methods in the Applied Sciences, Vol. 43, No. 16 Cross Ref Existence of the transformation operator by the decomposition methodApplicable Analysis, Vol. 84, No. 7 Cross Ref Differential operators for the solutions of complex partial differential equations29 May 2007 | Complex Variables, Theory and Application: An International Journal, Vol. 40, No. 3 Cross Ref Differential — Operator Solutions for Complex Partial Differential Equations Cross Ref Sampling theorems for higher order elliptic boundary value problems2 May 2007 | Applicable Analysis, Vol. 61, No. 1-2 Cross Ref On the analytic solutions of radially symmetric parabolic equations29 May 2007 | Complex Variables, Theory and Application: An International Journal, Vol. 28, No. 3 Cross Ref Sampling theorems associated with boundary value problems for elliptic partial differential equations in R n9 June 2010 | Complex Variables, Theory and Application: An International Journal, Vol. 23, No. 3-4 Cross Ref Differentialtransformatonen con lösungen partieller differentialgleichungen29 May 2007 | Complex Variables, Theory and Application: An International Journal, Vol. 18, No. 1-2 Cross Ref Some remarks on Newton-Sabatier methodsMathematical Methods in the Applied Sciences, Vol. 11, No. 1 Cross Ref On the determination of riemann functions30 January 2009 | Complex Variables, Theory and Application: An International Journal, Vol. 8, No. 3-4 Cross Ref Patterns and structure in systems governed by linear second-order differential equationsActa Applicandae Mathematicae, Vol. 6, No. 2 Cross Ref References Cross Ref The use of integral operators in undetermined coefficient problems for partial differential equations2 May 2007 | Applicable Analysis, Vol. 18, No. 4 Cross Ref Some Topics in Transmutation Cross Ref Algorithms for generalized cauchy kernels26 June 2007 | Complex Variables, Theory and Application: An International Journal, Vol. 2, No. 1 Cross Ref Integral Operators in the Function Theoretic Method for Partial Differential EquationsM. 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Cross Ref Volume 1, Issue 1| 1970SIAM Journal on Mathematical Analysis History Submitted:25 April 1969Published online:17 February 2012 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0501010Article page range:pp. 96-114ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics