5650 Solution by Definite Integrals 



Integration by means of simple solutions. 

 Somigliana, C. Mil. I. Lomb. Ed. 24 (1891) 

 1005-. 



of V 2 /=& 2 / for elliptic and parabolic co- 

 ordinates. Hartenstein, J. H. Arch. Mth. 

 Ps. 14 (1896) 170-. 



Integrations relating to elastic equilibrium. 

 Mathieu, E. L. Par. EC. Pol. J. Cah. 48 

 - (1880) 163-. 

 Laplace's equation, form, special. Niven, W. 



D. [1880] Mess. Mth. 10 (1881) 114-. 



, solution, particular. Jacobi, C. G. J. 

 Crelle J. 36 (1848) 113-. 



Maxwell's equations of electro-magnetic field, 

 solution. Fitzgerald, G. F. B. A. Ep. 

 (1890) 755-. 



Propagation of electricity. Poincare, H. C. 



E. 117 (1893) 1027-. 



, partial differential equation in. 

 Picard, E. C. E. 118 (1894) 16-. 



Solutions of (F 2 + fc 2 )^=0 in elliptic coordi- 

 nates, and physical applications. (F 2 written 

 for V 2 .) Maclaurin, R. C. [1898] Camb. Ph. 

 S. T. 17 (1899) 41-. 



V 4 k = 0, solutions in series. Marcolongo, E. 

 Nap. Ed. 28 (1889) 149-. 



<j> + -= ~ = 6 (t), electric interpretation. 



Eeignier, C., & Bary, P. Cherb. S. Sc. 

 Nt. Mm. 26 (1889) 65-. 



Dirichlet's Problem 5660 



Integration of V*u = Q (2 variables). Levi- 

 Civita, T. Tor. Ac. Sc. At. 33 (1897) 692- 

 or 932-. 



5650 Integration of the differen- 

 tial equations of mathematical 

 physics by definite integrals. 



5660 Dirichlet's problem and 

 analogous problems affected 

 by boundary conditions. 



Analytic theory of heat, problem in. Stekloff", 



W. C. E. 126 (1898) 1022-. 

 Boundary condition and discontinuities, func- 



tions determined from. Burnside, W. L. 



Mth. S. P. 22 (1891) 346-. 



conditions, determination of integrals of 

 partial differential equations by. Picard, E. 

 Par. S. Mth. Bll. 22 (1894) 103-. 



, given, determination of function in a 

 circle from. Veltmann, W. Z. Mth. Ps. 26 

 (1881) 1-. 



, , solutions of certain differential 

 equations satisfying. Brill, J. Camb. Ph. 

 S. P. 6 (1889) 344-. 



value problem for continuous plane curve 

 with no cusp. Noble, C. A. Gott. Nr. 

 (1896) 191-. 



Contour values, determination of integrals of 



differential equations by. Picard, E. C. 



E. 130 (1900) 447-. 

 -- , ---- linear equations, 2nd order, 



by. Picard, E. Liouv. J. Mth. 6 (1900) 



129-. 

 -- , ---- partial differential equations 



by. Picard, E. C. E. 109 (1889) 499-; 



Par. EC. Pol. J. 60 (1890) 89-; Liouv. J. 



Duhamel, J. M. C. Liouv. J. Mth. 19 (1854) Mth - 2 ( 1896 ) 295 ~ 

 337-. 



Definite integrals suggested by problems in 

 theory of electricity. Thomson, (Sir) W. 

 Camb. and Dubl. Mth. J. 2 (1847) 109-. 



Double definite integrals, employment in find- 

 ing the form of waves. Cauchy, A. L. C. 

 E. 13 (1841) 188-. 



Finite integrals of partial differential equations 

 occurring in physics. Earnshaw, S. Ph. 



, 2nd order, by. 



Picard, E. C. E. 128 (1899) 1487-. 

 Cooling of isotropic body, two theorems of 

 ' Andradez, . N. A. Mth. 8 



mg 



Mg. 4 (1877) 213-. 

 Fresnel's integrals, geometric significance. 



Umov, N. N. Es. S. Nt. Mm. (Mth.) 6 



(1885) 57-; Fschr. Ps. (1885) (Ab. 2) 15-. 

 Integration of V 2 u = on given Eiemann 



surface. Ascoli, G. [1887] Stpckh. Ak. 



Hndl. Bh. 13 (Afd, 1) (1888) No. 2, 83pp. 

 = (Ascoli). Enestrom, 



G. Stockh. Ofv. (1887) 99-; Fschr. Mth. 



(1887) 29. 

 V 4 u = (2 variables). Almansi, E. Tor. 



Ac. Sc. At. 31 (1895) 527- or 881-. 



= in a plane circular field. Lauri- 



cella, G. Tor. Ac. Sc. At. 31 (1895) 610- or 



1010-. 

 = (Lauricella and Almansi). Vol- 



terra, V. Tor. Ac. Sc. At. 31 (1895) 618- or 



1018-. 

 V 2 u + fc 2 M = on Eiemann surfaces. 



Sommerfeld, A. Gott. Nr. (1895) 267-. 



Poincare'. 



(1889) 435-. 

 Dirichlet's principle. Weierstrass, K. [1870] 



Wiad. Mt. 2 (1898) 1-. 

 -- . Phragmen, E. Stockh. Ofv. (1891) 



745-. 



-- . Arzela, C. Bologna Ed. 1 (1897) 71-. 

 -- . Volterra, V. Palermo Cir. Mt. Ed. 11 



(1897) 83-. 

 -- . Hilbert, D. D. Mth. Vr. Jbr. 8 (1900) 



(Heft 1) 184-. 



, application to function. Graf, J. H. 

 Bern Mt. (1891) 95-. 



in connection with V 2 u = ke u . Schulz, 

 W. N. Y. Am. Mth. S. Bll. 5 (1899) 219, 

 221-. 



t demonstration, new. Phragmen, E. 



Stockh. Ofv. (1892) 511-. 

 -- , , preliminary assumptions. Heine, E. 



Gott. Nr. (1871) 375-. 

 _ , , Eiemann's. Weber, H. [1869] 



Crelle J. 71 (1870) 29-. 



, generalisation. Eiemann, . C. E. 

 106 (1888) 123-. 



-- j substitute for. Dahvigk, F. von. Gott. 

 Nr. (1894) 160-. 



407 



