

Bibliography for the
Dirichlet Problem
unabridged
- 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.
- A computational approach for the analytical solving of a
Dirichlet-type problem for third order partial differential
equations
Guyer T.; Mirasyedioglu S.
Applied Mathematics and Computation, 10 May 2003, vol. 137, no. 1,
pp. 139-150(12), Ingenta.
- Solution of the Dirichlet boundary value problem for the
sine-Gordon equation
Leon J.
Physics Letters A, 10 June 2002, vol. 298, no. 4, pp. 243-252(10),
Ingenta.
- Solving Dirichlet's problem in a rectangle for separate
variable coefficient elliptic equations
Rodriguez M.J.; Rosello M.D.; Jerez S.; Jodar L.
Applied Mathematics Letters, August 2002, vol. 15, no. 6, pp.
693-696(4), Ingenta.
- A priori estimates of the solution for the Dirichlet
problem
Villacampa Y.; Balaguer A.
IMA Journal of Applied Mathematics, August 2002, vol. 67, no. 4,
pp. 371-382(12), Ingenta.
- 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.
- The Method of Integral Equations in the Mixed
Dirichlet--Neumann Problem for the Laplace Equation in the
Exterior of Cuts in the Plane
Krutitskii P.A.; Sgibnev A.I.
Differential Equations, October 2001, vol. 37, no. 10, pp.
1363-1375(13), Ingenta.
- 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.
- The Dirichlet Problem for the Total Variation Flow
Andreu F.; Ballester C.; Caselles V.; Mazón J.M.
Journal of Functional Analysis, March 2001, vol. 180, no. 2, pp.
347-403(57), Ingenta.
- Uniqueness of positive radial solutions of a semilinear
Dirichlet problem in an annulus
Yadava S.L.
Proceedings Section A: Mathematics - Royal Society of Edinburgh,
15 December 2000, vol. 130, no. 6, pp. 1417-1428(12),
Ingenta.
- Reflecting Brownian snake and a Neumann-Dirichlet problem
Abraham R.
Stochastic Processes and their Applications, October 2000, vol.
89, no. 2, pp. 239-260(22), Ingenta.
- 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.
- 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.
- A modified Green's-function technique for the exterior
Dirichlet problem in linear elasticity
Argyropoulos E.; Kiriaki K.; Roach G.
Quarterly Journal of Mechanics and Applied Mathematics, May 1998,
vol. 51, no. 2, pp. 275-296(22), Ingenta.
- The 2-dimensional Dirichlet problem in an external domain with
cuts.
Krutitskii, P. A.
Z. Anal. Anwendungen 17 (1998), no. 2, 361--378,
MathSciNet.
- Dirichlet's problems for biharmonic functions.
Zhao, Zhen; Quan, Chenfang
Beijing Shifan Daxue Xuebao 34 (1998), no. 2, 174--178,
MathSciNet.
- Path Integral Solution of the Dirichlet Problem
LaChapelle J.
Annals of Physics, March 1997, vol. 254, no. 2, pp. 397-418(22),
Ingenta.
- 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.
- 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.
- Global Existence for the Dirichlet Problem for the Viscous
Shallow Water Equations
Sundbye L.
Journal of Mathematical Analysis and Applications, August 1996,
vol. 202, no. 1, pp. 236-258(23), Ingenta.
- von Renteln, Michael Friedrich Prym (1841--1915)---and his
investigations on the Dirichlet problem.
Studies in the history of modern mathematics, II.
Rend. Circ. Mat. Palermo (2) Suppl. No. 44 (1996), 43--55,
MathSciNet.
- 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.
- Regularity of the Dirichlet problem in convex domains in the
plane.
Fromm, Stephen J.
Michigan Math. J. 41 (1994), no. 3, 491--507,
MathSciNet.
- 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.
- 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.
- Calculation of the normal derivative of the solution of the
Dirichlet problem for the Poisson equation. (Russian)
Kosmodem'yanskiui, A. A., Jr.
Dokl. Akad. Nauk 328 (1993), no. 2, 139--140; translation in
Russian Acad. Sci. Dokl. Math. 47 (1993), no. 1, 26--28,
MathSciNet.
- A method for solving the Dirichlet problem for domains with a
narrow slit. (Russian)
Vlasov, V. I.; Pal'tsev, A. B.
Dokl. Akad. Nauk 330 (1993), no. 2, 140--143; translation in
Russian Acad. Sci. Dokl. Math. 47 (1993), no. 3, 404--409,
MathSciNet.
- Boundary behavior of generalized Poisson integrals for the
half-space and the Dirichlet problem for the Schrödinger
operator.
Kheifits, Alexander I.
Proc. Amer. Math. Soc. 118 (1993), no. 4, 1199--1204,
MathSciNet.
- 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.
- 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.
- The Cauchy transform, the Szegö projection, the Dirichlet
problem, and the Ahlfors map.
Bell, S.
The Madison Symposium on Complex Analysis (Madison, WI, 1991),
43--61, Contemp. Math., 137, Amer. Math. Soc., Providence, RI,
1992, MathSciNet.
- The
Dirichlet Problem for a Disk (in Notes)
David Minda
American Mathematical Monthly, Vol. 97, No. 3. (Mar., 1990), pp.
220-223, Jstor.
- Analytic solution of the Dirichlet problem for T-shaped and
cross-shaped domains. (Russian)
Skorokhodov, S. L.
Analytic and numerical methods for solving problems in
mathematical physics (Russian), 58--70, Akad. Nauk SSSR, Vychisl.
Tsentr, Moscow, 1989, MathSciNet.
- 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.
- 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.
- 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.
- 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.
- The Dirichlet problem for the Poisson equation in an angular
domain. (Russian) Differentsial'nye
Vlasov, V. I.; Volkov, D. B.
Uravneniya 21 (1985), no. 12, 2105--2114, 2204,
MathSciNet.
- The exterior Dirichlet problem for the Laplace equation.
Ahner, J. F.
Math. Methods Appl. Sci. 7 (1985), no. 4, 461--469,
MathSciNet.
- 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.
- 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.
- The Dirichlet Problem: A Mathematical
Development
Goulet, John
Pi Mu Epsilon J., (1983), V. 7, No. 8, pp. 502-511.
- 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.
- 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.
- 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.
- Solutions of a nonlinear Dirichlet problem for nearly circular
domains.
Bandle, Catherine
SIAM J. Numer. Anal. 20 (1983), no. 6, 1094--1098,
MathSciNet.
- The Dirichlet problem on some conformally invariant bicompact
extensions of a plane domain. (Russian)
Ivanov, O. V.; Suvorov, G. D.
Dokl. Akad. Nauk Ukrain. SSR Ser. A 1982, no. 1, 16--19,
MathSciNet.
- The
Lagrange Multiplier Method for Dirichlet's
Problem
James H. Bramble
Mathematics of Computation, Vol. 37, No. 155. (Jul., 1981), pp.
1-11, Jstor.
- The
Dirichlet Problem for Harmonic
Functions
Ivan Netuka
American Mathematical Monthly, Vol. 87, No. 8. (Oct., 1980), pp.
621-628, Jstor.
- The Dirichlet Problem
Garding, Lars
Math. Intell., (1979), V. 2, No. 1, pp. 43-53.
- On delta-analytic functions and the numerical solution of the
Dirichlet problem.
Sonnenschein, J.
Vorträge der Wissenschaftlichen Jahrestagung der Gesellschaft
für Angewandte Mathematik und Mechanik, Teil I (Brussels,
1978). Z. Angew. Math. Mech. 59 (1979), no. 3, T82--T83,
MathSciNet.
- On generalised Poisson's integral and Dirichlet problem.
Sen, S.
Math. Ed. (Siwan) 12 (1978), no. 2, A41--A46,
MathSciNet.
- A solution of the biharmonic Dirichlet problem by means of
hypercomplex analytic functions.
Edenhofer, J.
Function theoretic methods for partial differential equations
(Proc. Internat. Sympos., Darmstadt, 1976), pp. 192--202. Lecture
Notes in Math., Vol. 561, Springer, Berlin, 1976,
MathSciNet.
- 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.
- 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.
- 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.
- A
Dirichlet Problem
Clarence R. Edstrom
Mathematics Magazine, Vol. 45, No. 4. (Sep., 1972), pp. 204-205,
Jstor.
- 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.
- 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.
- 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.
- Solvable
Functions for the Dirichlet Problem
Ernest C. Schlesinger
American Journal of Mathematics, Vol. 84, No. 2. (Apr., 1962), pp.
317-323, Jstor.
- On the solution of the Dirichlet problem for multiply
connected regions. (Russian)
Kazban, A. M.
Trudy Kazan. Aviacion. Inst. Vyp. 71 1962 56--72,
MathSciNet.
- Numerical
Analysis and the Dirichlet Problem
Donald Greenspan
Mathematics Magazine, Vol. 32, No. 4. (Mar. - Apr., 1959), pp.
177-188, Jstor.
- On
the Numerical Solution of Dirichlet-Type
Problems
Donald Greenspan
American Mathematical Monthly, Vol. 66, No. 1. (Jan., 1959), pp.
40-46, Jstor.
- On the behavior of the solution of the Dirichlet problem at
analytic corners.
Laasonen, Pentti
Ann. Acad. Sci. Fenn. Ser. A. I. 1957 (1957), no. 241, 13 pp.,
MathSciNet.
- 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.
- Dirichlet problems on Riemann surfaces and conformal
mappings.
Ohtsuka, Makoto
Nagoya Math. J. 3, (1951). 91--137,
MathSciNet.
- The Dirichlet problem for multiply connected domains.
Reynolds, R. R.
J. Math. Physics 30, (1951). 11--22,
MathSciNet.
- On
Dirichlet's Problem
C. Caratheodory
American Journal of Mathematics, Vol. 59, No. 4. (Oct., 1937), pp.
709-731, Jstor.
- On
the Dirichlet-Neumann Problem
G. E. Raynor
The Annals of Mathematics, 2nd Ser., Vol. 32, No. 1. (Jan., 1931),
pp. 17-22, Jstor.
- An
Intrinsic Treatment of Poisson's
Integral
Fred W. Perkins
American Journal of Mathematics, Vol. 50, No. 3. (Jul., 1928), pp.
389-414, Jstor.
- 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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