The Dirichlet problem for a singular elliptic equation
Annales de l'Institut Fourier, Volume 26 (1976) no. 1, pp. 205-224.

We study the solvability of the Dirichlet problem for a linear elliptic operator of the second order in which the coefficients of the first order derivatives become infinite on a portion of the boundary. The study makes use of Schauder’s estimates and suitably constructed barriers.

On étudie l’existence de solution du problème de Dirichlet pour un opérateur elliptique linéaire du second ordre dont les coefficients des dérivées du premier ordre deviennent infinis sur une partie de la frontière. On utilise les estimations de Schauder et des barrières convenablement construites.

@article{AIF_1976__26_1_205_0,
     author = {C\'ac, Nguyen Phuong},
     title = {The {Dirichlet} problem for a singular elliptic equation},
     journal = {Annales de l'Institut Fourier},
     pages = {205--224},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {26},
     number = {1},
     year = {1976},
     doi = {10.5802/aif.604},
     mrnumber = {53 #6088},
     zbl = {0312.35028},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.604/}
}
TY  - JOUR
AU  - Các, Nguyen Phuong
TI  - The Dirichlet problem for a singular elliptic equation
JO  - Annales de l'Institut Fourier
PY  - 1976
SP  - 205
EP  - 224
VL  - 26
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.604/
DO  - 10.5802/aif.604
LA  - en
ID  - AIF_1976__26_1_205_0
ER  - 
%0 Journal Article
%A Các, Nguyen Phuong
%T The Dirichlet problem for a singular elliptic equation
%J Annales de l'Institut Fourier
%D 1976
%P 205-224
%V 26
%N 1
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.604/
%R 10.5802/aif.604
%G en
%F AIF_1976__26_1_205_0
Các, Nguyen Phuong. The Dirichlet problem for a singular elliptic equation. Annales de l'Institut Fourier, Volume 26 (1976) no. 1, pp. 205-224. doi : 10.5802/aif.604. http://archive.numdam.org/articles/10.5802/aif.604/

[1] M.S. Baouendi, Sur une classe d'opérateurs elliptiques dégénérés, Bull. Soc. Math. France, 95 (1967), 45-87. | Numdam | MR | Zbl

[2] P. Brousse and H. Poncin, Quelques résultats généraux concernant la détermination de solutions d'équations elliptiques par les conditions aux frontières, Jubilé Scientifique de M.P. Riabonchinsky, Publ. Sci. et techn. du Ministère de l'Air, Paris, 1954.

[3] A. Huber, Some results on generalized axially symmetric potentials, Proceedings of the Conference on Differential Equations, University of Maryland, 1955. | Zbl

[4] P. Jamet and S. V. Parter, Numerical methods for elliptic differential equations whose coefficients are singular on a portion of the boundary, Siam J. Numer. Anal., 4 (1967), 131-146. | MR | Zbl

[5] J.J. Kohn and L. Nirenberg, Non coercive boundary value problems, Comm. Pure Appl. Math., 18 (1965), 443-492. | MR | Zbl

[6] O.A. Ladyzhenskaya and N.N. Uraltseva, Linear and quasilinear and quasilinear elliptic equations, Translated from the Russian, Academic Press, New York 1968. | MR | Zbl

[7] C.Y. Lo, Dirichlet problems for singular elliptic equations, Proc. Amer. Math. Soc., 39 (1973), 337-342. | MR | Zbl

[8] C. Miranda, Partial Differential Equations of Elliptic Type, Springer-Verlag, New York 1970. | MR | Zbl

[9] H. Morel, Introduction de poids dans l'étude des problèmes aux limites, Ann. Inst. Fourier, Grenoble, 12 (1962), 299-414. | Numdam | MR | Zbl

[10] M.H. Protter and H.F. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, New Jersey 1967. | MR | Zbl

[11] M.K.V. Murthy and G. Stampacchia, Boundary value problems for some degenerate elliptic operators, Ann. Math. Pura Appl. 80 (1968), 1-122. | MR | Zbl

[12] M. Schechter, On the Dirichlet problem for second order equations with coefficients singular at the boundary, Comm. Pure Appl. Math., 13 (1960), 321-328. | MR | Zbl

Cited by Sources: