@article{AFST_1996_6_S5__57_0, author = {Korevaar, Jacob}, title = {Electrostatic fields due to distributions of electrons}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {57--76}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, S5}, year = {1996}, mrnumber = {1462707}, zbl = {0893.31005}, language = {en}, url = {http://www.numdam.org/item/AFST_1996_6_S5__57_0/} }
TY - JOUR AU - Korevaar, Jacob TI - Electrostatic fields due to distributions of electrons JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 1996 SP - 57 EP - 76 VL - S5 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/item/AFST_1996_6_S5__57_0/ LA - en ID - AFST_1996_6_S5__57_0 ER -
%0 Journal Article %A Korevaar, Jacob %T Electrostatic fields due to distributions of electrons %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 1996 %P 57-76 %V S5 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/item/AFST_1996_6_S5__57_0/ %G en %F AFST_1996_6_S5__57_0
Korevaar, Jacob. Electrostatic fields due to distributions of electrons. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome S5 (1996), pp. 57-76. http://www.numdam.org/item/AFST_1996_6_S5__57_0/
[1] On quadrature formulas with positive coefficients, Izv. Akad. Nauk SSSR (Russian), Ser. Mat. 1, n° 4 ( 1937), pp. 479-503 | JFM
.-;Collected Works, vol. II. Izdat. Akad. Nauk SSSR. Moscow, 1954, pp. 205-227; See also the announcements 'Sur les formules de quadrature à coefficients non négatifs et abscisses équidistantes' and 'Modifications de la formule de quadrature de Tchebycheff' in C.R. Acad. Sci. Paris 204 (1937), pp. 1294-1296 and 1526-1529. | MR | Zbl
[2] Estimates of harmonic measure , Arch. Rat. Mech. Anal. 65 (1977), pp. 275-288. | MR | Zbl
.-[3] On the distribution of Fekete points, Duke Math. J. 45 (1978), pp. 537-542. | MR | Zbl
.-[4] Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), pp. 228-249. | EuDML | JFM | MR
.-[5] Potentiel d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions, Dissertation , Lunds Univ. Mat. Sem. 3 (1935), pp. 1-118. | JFM | Zbl
.-[6] An extended principle of the maximum for harmonic functions in 3 dimensions, J. London Math. Soc. 30 (1955), pp. 388-401. | MR | Zbl
.-[7] A result concerning convex level surfaces of 3-dimensional harmonic functions, J. London Math. Soc. 32 (1957), pp. 286-294. | MR | Zbl
.-[8] Elliptic partial differential equations of second order, Grundl. d. math. Wiss. 224, Springer-Verlag, New York, 1977. | MR | Zbl
and -[9] Rearrangements and convexity of level sets in PDE, Lecture Notes in Math. 1150, Springer, Berlin , 1985. | MR | Zbl
.-[10] Asymptotically neutral distributions of electrons and polynomial approximation, Ann. of Math. 80 (1964), pp. 403-410. | MR | Zbl
.-[11] Equilibrium distributions of electrons on roundish plane conductors I, II, Indag. Math. 36 (1974), pp. 423-456. | MR | Zbl
.-[12] Problems of equilibrium points on the sphere and electrostatic fields, Univ. of Amsterdam , Math. Dept. Report 1976-03.
.-[13] Chebyshev-type quadratures: use of complex analysis and potential theory, in: Complex potential theory (P. M. Gauthier and G. Sabidussi, eds.), Kluwer, Dordrecht, 1994, pp. 325-364. | MR | Zbl
.-[14] Fields due to electrons on an analytic curve, SIAM J. Math. Anal. 2 (1971), pp. 445-453. | MR | Zbl
and .-[15] Equilibrium distributions of electrons on smooth plane conductors, Indag. Math. 45 (1983), pp. 203-219. | MR | Zbl
and .-[16] Spherical Faraday cage for the case of equal point charges and Chebyshev-type quadrature on the sphere, Integral Transforms and Special Functions 1 (1993), pp. 105-117. | MR | Zbl
and .-[17] Electrostatic fields due to distributions of equal point charges on convex conductors in R3 with minimal energy. Math. Dept., Univ. of Amsterdam, Preprint, 1995.
and .-[18] Convexity of level sets for solutions to elliptic ring problems, Comm. Partial Differential Equations 15 (1990), pp. 541-556. | MR | Zbl
.-[19] On the distribution of Fekete points II, Mathematika 18 ( 1971), pp. 40-49. | MR | Zbl
.-[20] On the distribution of Fekete points, Mathematika 15 (1968), pp. 70-75. | MR | Zbl
and .-[21] Studies in potential theory, Ph. D. thesis, Free University, Amsterdam , 1995.
.-[22] Über den transfiniten Durchmesser (Kapazitätskonstante) von ebenen und räumlichen Punktmengen, J. reine und angew. Math. 165 ( 1931), pp. 4-49. | JFM | Zbl
and .-[23] Polynome und konforme Abbildung , Monatsh. Math. 69 ( 1965), pp. 58-61. | MR | Zbl
. -[24] Über die Verteilung der Fekete-Punkte , Math. Ann. 168 ( 1967), pp. 111-127. | MR | Zbl
.-[25] Über die Verteilung der Fekete-Punkte II, Math. Ann. 179 ( 1969), pp. 212-218. | MR | Zbl
.-[26] Sur la distribution de l'électricité à la surface des conducteurs fermés et des conducteurs ouverts, Ann. École Norm. Sup. (3) 3 (1886), Supplément. | JFM | Numdam
. -[27] Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 1 (1918), pp. 377-402. | JFM | MR
. -[28] On the regularity of the distribution of the Fekete points of a compact surface in Rn, Ark. Mat. 11 (1973), pp. 147-151. | MR | Zbl
. -[29] Sur certains polynômes qui vérifient une équation différentielle linéaire du second ordre et sur la théorie des fonctions de Lamé, Acta Math. 6 (1885), pp. 321-326 | JFM
. -; Œuvres Complètes, vol. I. Noordhoff, Groningen, 1914, pp. 434-439; Œuvres Complètes - Collected Papers, vol. I (enlarged edition, G. van Dijk, ed.) ; Springer, Berlin, 1993, pp. 522-527.
[30] Sur quelques théorèmes d'algèbre , C.R. Acad. Sci. Paris 100 (1885), pp. 439-440 | JFM
.-; Œuvres Complètes, vol. I, pp. 440-441; Œuvres Complètes - Collected Papers, vol. I, pp. 528-529.
[31] Sur les polynômes de Jacobi, C.R. Acad. Sci. Paris 100 ( 1885 ), pp. 620-622 | JFM
.-; Œuvres Complètes, vol. I, pp. 442-444; Œuvres Complètes - Collected Papers, vol. I, pp. 530-532.
[32] Sur les racines de l'équation Xn = 0, Acta Math. 9 (1886), pp. 385-400 | JFM
.-; Œuvres Complètes, vol. II. Noordhoff, Groningen, 1918, pp. 73-88
; Œuvres Complètes - Collected Papers, vol. II (enlarged edition, G. van Dijk. ed.); Springer, Berlin, 1993, pp. 77-92.
[33] Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. 23; Providence, R.I., Fourth edition, 1975 . | MR
.-[34] The impact of Stieltjes' work on continued fractions and orthogonal polynomials, In: T. J. Stieltjes, Œuvres Complètes - Collected Papers . vol. I (enlarged edition, G. van Dijk, ed.). Springer, Berlin, 1993, pp. 5-37.
.-[35] On the boundary values of harmonic functions in R3, Arkiv för Mat. 5, n° 14 (1964), pp. 221-230. | MR | Zbl
.-[36] Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand. 21 (1967), pp. 17-37. | MR | Zbl
.-