5660 



Dirichlet's Problem and its Analogues 



5560 



Dirichlet's principle, substitute for, in certain 

 cases. Neumann, C. Leip. Mth. Ps. B. 47 

 (1895) 185-. 



problem. Riemann, J. Par. EC. Norm. A. 

 5 (1888) 327-. 



. Grave, D. A. As. Fr. C. R. (1895) 



(Pt. 2) 111-. 



. Zaremba, S. Par. EC. Norm. A. 14 

 (1897) 251-. 



. Fredholm, I. Stockh. Ofv. (1900) 39-. 



__. ,. . 

 Integration of 



= under given con- 



ditions as to boundary and discontinuity. 



Schwarz, H. A. Berl. Mb. (1870) 767-. 

 = . Prym, F. E. Crelle J. 73 



(1871) 340-. 

 V 2 u = within a circular area. Ascoli, G. 



Mil. I. Lomb. Rd. 17 (1884) 627-. 

 = for some simple areas. Ascoli, 



G. Mil. I. Lomb. Rd. 18 (1885) 252-. 



-- for 2 dimensions, special case. Kluyver, --- = in any Riemann area. Ascoli, 

 J. C. Acta Mth. 21 (1897) 265-. 



in domains, with discontinuous boun- 

 daries. Schwarz, H. A. Ziir. Vjschr. 15 

 (1870) 272-. 



and its extension to general linear 

 equations, 2nd order. Paraf, A. Toul. 

 Fac. Sc. A. 6 (1892) H, 75 pp. 



, generalisation, and linear partial dif- 

 ferential equations, 2nd order. Picard, E. 

 C. R. 130 (1900) 1088-. 



and harmonic functions belonging to 

 closed surface. Le Roy, . C. R. 123 

 (1896) 986-. 



, questions relating to. Liapounoff, A. 

 C. R. 125 (1897) 808- ; Liouv. J. Mth. 4 

 (1898) 241-. 



-- , solutions by combination of Neumann's 



and Schwarz 's methods. Kohn, A. Mth. 



A. 53 (1900) 593-. 

 Distribution of electricity, problem of. Poin- 



care, H. C. R. 104 (1887) 44-. 



, , and Neumann's problem. 

 Stekloff, W. C. R. 125 (1897) 1026-. 



Equation of vibrations of a membrane. Poin- 



care, H. C. R. 118 (1894) 447-. 

 Equations of conduction of heat, integration. 



Le Roy, E. Par. EC. Norm. A. 14 (1897) 



379-; 15 (1898) 9-. 

 Fundamental functions and Dirichlet'sproblem. 



Stekloff, W. C. R. 131 (1900) 870-. 

 -- , existence. Stekloff, W. C. R. 128 (1899) 



808-. 

 -- .theory. Stekloff, W. C.R. 128 (1899) 984-. 



problems of mathematical physics. Stekloff, 

 W. C. R. 128 (1899) 588-. 



----- , general methods for solution. 



Stekloff, W. Toul. Fac. Sc. A. 2 (1900) 207-. 

 Green's function, behaviour at limit of its 



region. Neumann, C. Leip. Mth. Ps. B. 



40 (1888) 163-. 

 -- for system of non-intersecting spheres. 



Burnside, W. L. Mth. S. P. 25 (1894) 94-. 

 -- , theory. Zaremba, . Par. S. Mth. 



Bll. 24 (1896) 19-. 



functions in 1 dimension. Burkhardt, H. 

 Par. S. Mth. Bll. 22 (1894) 71-. 



second function. Arcais, F. d\ Ven. I. 

 At. (1897-98) 1664-. 



Integrals of Laplace's equation. Capelli, A. 

 G. Mt. 23 (1885) 123-. 



Integration of 3- 



-r 

 dt/ 2 



Neumann, C. 



Crelle J. 59 (1861) 335-. 



Mth. A. 1 (1869) 1-. 



Weber ' 



G. Mil. I. Lomb. Rd. 18 (1885) 718-. 

 = . Ohnesorge, 0. Arch. Mth. Ps. 



2 (1885) 53-. 

 V 4 u = for plane regions. Venske, 0. 



Gott. Nr. (1891) 27-. 

 V*u=fu. Lindeberg, J. W. C. R. 130 



(1900) 1539-. 

 V 2 w=e" on a closed surface. Picard, E. 



Bll. Sc. Mth. 24 (1900) 196-. 

 Inverse square, actions following law of. 



Vaschy, . As. Fr. C. R. (1894) (Pt. 2) 



141-. 

 Method of arithmetical mean. Neumann, C. 



Leip. Mth. Ps. Ab. 13 (1887) 705- ; 14 (1888) 



563-. 



, Neumann's. Tauber, A. Mh. 



Mth. Ps. 5 (1894) 137-. 



, . Stekloff, W. C. R. 131 (1900) 



987-, 1182-. 



successive approximations, Picard's. 

 Zaremba, S. C. R. 124 (1897) 554-. 



Neumann's and Gauss's problems. Stekloff, 

 W. C. R. 130 (1900) 480-. 



method and Dirichlet's problem. Poiucare, 

 H. [1895] Acta Mth. 20 (1897) 59-. 



. Stekloff, W. C. R. 130 (1900) 



396-, 1599-. 



. Korn, A. C. R. 130 (1900) 



557, 1238- ; 131 (1900)26-. 



(Korn). Stekloff, W. C. R. 



130 (1900) 826-. 



of solving Dirichlet's problem. La Vallee- 



Poussin, C. de. Brux. S. Sc. A. 18 (1894) 

 (Pt. 1) 11-. 



Partial differential equation in theory of mem- 

 branes. Picard, E. C. R. 117 (1893) 502-. 



equations, 2nd order, with imaginary 

 characteristics. Picard, E. C. R. 122 (1896) 

 417-. 



Poisson's integral. Bncher, M. N. Y. Am. 



Mth. S. Bll. 4 (1898) 424-. 

 Potential, existence, proof. Kirchhoff, G. Acta 



Mth. 14 (1890-91) 179-. 



function in plane space bounded by two 

 circles with given values at boundaries. 

 Kluyver, J. C. N. Arch. Wisk. 3 (1898) 

 230- ; Fschr. Mth. (1897) 363-. 



functions expressed in curvilinear coordi- 

 nates. Painleve, P. [1889] Lille Tr. Mm. 

 1 (1889-91) Mem. 1, 28 pp. 



theory, solution of fundamental problem in. 

 Schiitz, J. R. Gott. Nr. (1895) 1-. 



Problem of hydrodynamics. Lejeune-Dirichlet, 

 G. [1857] Gott. Ab. 8 (1858-59) (Mth.) 3-. 



, Dirichlet's. Dedekind, R. [1860] 



Crelle J. 58 (1861) 217-. 



408 



