The Dirichlet problem for a singular elliptic equation

Nguyen Phuong Các

Annales de l'institut Fourier (1976)

  • Volume: 26, Issue: 1, page 205-224
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Các, Nguyen Phuong. "The Dirichlet problem for a singular elliptic equation." Annales de l'institut Fourier 26.1 (1976): 205-224. <http://eudml.org/doc/74266>.

@article{Các1976,
abstract = {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.},
author = {Các, Nguyen Phuong},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {205-224},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Dirichlet problem for a singular elliptic equation},
url = {http://eudml.org/doc/74266},
volume = {26},
year = {1976},
}

TY - JOUR
AU - Các, Nguyen Phuong
TI - The Dirichlet problem for a singular elliptic equation
JO - Annales de l'institut Fourier
PY - 1976
PB - Association des Annales de l'Institut Fourier
VL - 26
IS - 1
SP - 205
EP - 224
AB - 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.
LA - eng
UR - http://eudml.org/doc/74266
ER -

References

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  1. [1] M.S. BAOUENDI, Sur une classe d'opérateurs elliptiques dégénérés, Bull. Soc. Math. France, 95 (1967), 45-87. Zbl0179.19501MR37 #4398
  2. [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. [3] A. HUBER, Some results on generalized axially symmetric potentials, Proceedings of the Conference on Differential Equations, University of Maryland, 1955. Zbl0072.31406
  4. [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. Zbl0161.35804MR35 #6383
  5. [5] J.J. KOHN and L. NIRENBERG, Non coercive boundary value problems, Comm. Pure Appl. Math., 18 (1965), 443-492. Zbl0125.33302MR31 #6041
  6. [6] O.A. LADYZHENSKAYA and N.N. URALTSEVA, Linear and quasilinear and quasilinear elliptic equations, Translated from the Russian, Academic Press, New York 1968. Zbl0164.13002MR39 #5941
  7. [7] C.Y. LO, Dirichlet problems for singular elliptic equations, Proc. Amer. Math. Soc., 39 (1973), 337-342. Zbl0264.35034MR47 #5443
  8. [8] C. MIRANDA, Partial Differential Equations of Elliptic Type, Springer-Verlag, New York 1970. Zbl0198.14101MR44 #1924
  9. [9] H. MOREL, Introduction de poids dans l'étude des problèmes aux limites, Ann. Inst. Fourier, Grenoble, 12 (1962), 299-414. Zbl0112.33903MR29 #1558
  10. [10] M.H. PROTTER and H.F. WEINBERGER, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, New Jersey 1967. Zbl0153.13602MR36 #2935
  11. [11] M.K.V. MURTHY and G. STAMPACCHIA, Boundary value problems for some degenerate elliptic operators, Ann. Math. Pura Appl. 80 (1968), 1-122. Zbl0185.19201MR40 #3069
  12. [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. Zbl0106.07703MR22 #3872

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