Bibliography for the Dirichlet Problem

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  1. Existence of solutions for p(x)-Laplacian Dirichlet problem
    Fan X.-L.; Zhang Q.-H.
    Nonlinear Analysis, March 2003, vol. 52, no. 8, pp. 1843-1852(10), Ingenta.  
  2. On identifying Dirichlet condition for under-determined problem of the Laplace equation by BEM
    Ohura Y.; Wang Q.; Onishi K.
    Engineering Analysis with Boundary Elements, January 2002, vol. 26, no. 1, pp. 87-94(8), Ingenta.  
  3. The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral
    Matevosyan O.A.
    Mathematical Notes, 10 September 2001, vol. 70, no. 3/4, pp. 363-377(15), Ingenta.  
  4. The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts.  
    Krutitskii, P. A.
    Proc. Edinburgh Math. Soc. (2)  43  (2000),  no. 2, 325--341, MathSciNet.   
  5. Solution of the Dirichlet Problem for the Laplace equation
    Medková D.
    Applications of Mathematics, April 1999, vol. 44, no. 2, pp. 143-168(26), Ingenta.  
  6. Dirichlet's problems for biharmonic functions.
    Zhao, Zhen; Quan, Chenfang
    Beijing Shifan Daxue Xuebao 34 (1998), no. 2, 174--178, MathSciNet.   
  7. Path Integral Solution of the Dirichlet Problem
    LaChapelle J.
    Annals of Physics, March 1997, vol. 254, no. 2, pp. 397-418(22), Ingenta.  
  8. Radial Solutions to a Dirichlet Problem Involving Critical Exponents When N = 6  
    Alfonso Castro; Alexandra Kurepa  
    Transactions of the American Mathematical Society, Vol. 348, No. 2. (Feb., 1996), pp. 781-798, Jstor.  
  9. On the mixed initial Dirichlet - Neumann problem for the wave equation in the circle
    Sheikh M.G.E.
    Journal of Physics A: Mathematical and General, 1996, vol. 29, no. 3, pp. 595-606(12), Ingenta.  
  10. Radially Symmetric Solutions to a Dirichlet Problem Involving Critical Exponents  
    Alfonso Castro; Alexandra Kurepa  
    Transactions of the American Mathematical Society, Vol. 343, No. 2. (Jun., 1994), pp. 907-926, Jstor.  
  11. On the Solution of the Dirichlet Problem for the Two-Dimensional Laplace Equation  
    Christian Constanda  
    Proceedings of the American Mathematical Society, Vol. 119, No. 3. (Nov., 1993), pp. 877-884, Jstor.  
  12. Multigrid Preconditioning for the Biharmonic Dirichlet Problem (in Special Section on Multigrid Methods)  
    M. R. Hanisch  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 1. (Feb., 1993), pp. 184-214, Jstor.  
  13. Singularities encountered by the analytic continuation of solutions to Dirichlet's problem.
    Ebenfelt, Peter
    Complex Variables Theory Appl. 20 (1992), no. 1-4, 75--91, MathSciNet.   
  14. An Adapted Boundary Element Method for the Dirichlet Problem in Polygonal Domains  
    M. Bourlard; S. Nicaise; L. Paquet  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 3. (Jun., 1991), pp. 728-743, Jstor.  
  15. The Dirichlet Problem for a Disk (in Notes)  
    David Minda  
    American Mathematical Monthly, Vol. 97, No. 3. (Mar., 1990), pp. 220-223, Jstor.  
  16. An Example of Nonhomotopic Solutions to the Dirichlet Problem for Harmonic Maps in Two Dimensions  
    Luc Oswald; George Paulik  
    Proceedings of the American Mathematical Society, Vol. 104, No. 4. (Dec., 1988), pp. 1267-1270, Jstor.  
  17. Nonnegative Solutions of the Initial-Dirichlet Problem for Generalized Porous Medium Equations in Cylinders  
    Bjorn E. J. Dahlberg; Carlos E. Kenig  
    Journal of the American Mathematical Society, Vol. 1, No. 2. (Apr., 1988), pp. 401-412, Jstor.  
  18. Generalized Difference Methods for a Nonlinear Dirichlet Problem  
    Li Ronghua  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 1. (Feb., 1987), pp. 77-88, Jstor.  
  19. A Heuristic for the Poisson Integral for the Half Plane and some Caveats (in The Teaching of Mathematics)  
    Ridgley Lange; Robert A. Walsh  
    American Mathematical Monthly, Vol. 92, No. 5. (May, 1985), pp. 356-358, Jstor.  
  20. An Exterior Dirichlet Problem with Applications to Some Nonlinear Equations Arising in Geometry  
    Carlos E. Kenig; Wei-Ming Ni  
    American Journal of Mathematics, Vol. 106, No. 3. (Jun., 1984), pp. 689-702, Jstor.  
  21. Probabilistic Solution of the Dirichlet Problem for Biharmonic Functions in Discrete Space  
    R. J. Vanderbei  
    Annals of Probability, Vol. 12, No. 2. (May, 1984), pp. 311-324, Jstor.  
  22. The Dirichlet Problem: A Mathematical Development  
    Goulet, John  
    Pi Mu Epsilon J., (1983), V. 7, No. 8, pp. 502-511.
  23. Estimates of Caloric Measure and the Initial-Dirichlet Problem for the Heat Equation in Lipschitz Cylinders  
    Eugene Fabes; Sandro Salsa  
    Transactions of the American Mathematical Society, Vol. 279, No. 2. (Oct., 1983), pp. 635-650, Jstor.  
  24. Harmonic Functions and the Dirichlet Problem for Revival Markov Processes  
    Kyle Siegrist  
    Annals of Probability, Vol. 11, No. 3. (Aug., 1983), pp. 624-634, Jstor.  
  25. Fast Numerical Solution of the Biharmonic Dirichlet Problem on Rectangles  
    Petter Bjorstad  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 1. (Feb., 1983), pp. 59-71, Jstor.  
  26. The Lagrange Multiplier Method for Dirichlet's Problem  
    James H. Bramble  
    Mathematics of Computation, Vol. 37, No. 155. (Jul., 1981), pp. 1-11, Jstor.  
  27. The Dirichlet Problem for Harmonic Functions  
    Ivan Netuka  
    American Mathematical Monthly, Vol. 87, No. 8. (Oct., 1980), pp. 621-628, Jstor.  
  28. The Dirichlet Problem  
    Garding, Lars  
    Math. Intell., (1979), V. 2, No. 1, pp. 43-53.
  29. A Galerkin Method for a Nonlinear Dirichlet Problem  
    Jim Douglas, Jr; Todd Dupont  
    Mathematics of Computation, Vol. 29, No. 131. (Jul., 1975), pp. 689-696, Jstor.  
  30. Some Half-Plane Dirichlet Problems: A Bare Hands Approach (in Classroom Notes)  
    F. J. Flanigan  
    American Mathematical Monthly, Vol. 80, No. 1. (Jan., 1973), pp. 59-61, Jstor.  
  31. Simplified Proofs of Error Estimates for the Least Squares Method for Dirichlet's Problem  
    Garth A. Baker  
    Mathematics of Computation, Vol. 27, No. 122. (Apr., 1973), pp. 229-235, Jstor.  
  32. A Dirichlet Problem  
    Clarence R. Edstrom  
    Mathematics Magazine, Vol. 45, No. 4. (Sep., 1972), pp. 204-205, Jstor.  
  33. The Approximate Solution of the Dirichlet Problem by Means of Integral Equations  
    George A. Costello  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 1. (Mar., 1971), pp. 135-136, Jstor.  
  34. The Poisson Integral for Generalized Half-Planes and Bounded Symmetric Domains  
    Adam Koranyi  
    The Annals of Mathematics, 2nd Ser., Vol. 82, No. 2. (Sep., 1965), pp. 332-350, Jstor.  
  35. The Numerical Solution of the Dirichlet Problem for Laplace's Equation by Linear Programming  
    J. R. Cannon  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 1. (Mar., 1964), pp. 233-237, Jstor.  
  36. Solvable Functions for the Dirichlet Problem  
    Ernest C. Schlesinger  
    American Journal of Mathematics, Vol. 84, No. 2. (Apr., 1962), pp. 317-323, Jstor.  
  37. Numerical Analysis and the Dirichlet Problem  
    Donald Greenspan  
    Mathematics Magazine, Vol. 32, No. 4. (Mar. - Apr., 1959), pp. 177-188, Jstor.  
  38. On the Numerical Solution of Dirichlet-Type Problems  
    Donald Greenspan  
    American Mathematical Monthly, Vol. 66, No. 1. (Jan., 1959), pp. 40-46, Jstor.  
  39. Some Continuous Monte Carlo Methods for the Dirichlet Problem  
    Mervin E. Muller  
    Annals of Mathematical Statistics, Vol. 27, No. 3. (Sep., 1956), pp. 569-589, Jstor.  
  40. Dirichlet problems on Riemann surfaces and conformal mappings.
    Ohtsuka, Makoto
    Nagoya Math. J. 3, (1951). 91--137, MathSciNet.   
  41. On Dirichlet's Problem  
    C. Caratheodory  
    American Journal of Mathematics, Vol. 59, No. 4. (Oct., 1937), pp. 709-731, Jstor.  
  42. On the Dirichlet-Neumann Problem  
    G. E. Raynor  
    The Annals of Mathematics, 2nd Ser., Vol. 32, No. 1. (Jan., 1931), pp. 17-22, Jstor.  
  43. An Intrinsic Treatment of Poisson's Integral  
    Fred W. Perkins  
    American Journal of Mathematics, Vol. 50, No. 3. (Jul., 1928), pp. 389-414, Jstor.  
  44. The Poisson Integral and an Analytic Function on Its Circle of Convergence  
    A. Arwin  
    The Annals of Mathematics, 2nd Ser., Vol. 23, No. 2. (Dec., 1921), pp. 141-143, Jstor.  

 

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(c) John H. Mathews 2003