Existence and estimates of Green's function for degenerate elliptic equations

S. Chanillo; R. L. Wheeden

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1988)

  • Volume: 15, Issue: 2, page 309-340
  • ISSN: 0391-173X

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Chanillo, S., and Wheeden, R. L.. "Existence and estimates of Green's function for degenerate elliptic equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 15.2 (1988): 309-340. <http://eudml.org/doc/84032>.

@article{Chanillo1988,
author = {Chanillo, S., Wheeden, R. L.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {degenerate operators in divergence form; Green's function},
language = {eng},
number = {2},
pages = {309-340},
publisher = {Scuola normale superiore},
title = {Existence and estimates of Green's function for degenerate elliptic equations},
url = {http://eudml.org/doc/84032},
volume = {15},
year = {1988},
}

TY - JOUR
AU - Chanillo, S.
AU - Wheeden, R. L.
TI - Existence and estimates of Green's function for degenerate elliptic equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1988
PB - Scuola normale superiore
VL - 15
IS - 2
SP - 309
EP - 340
LA - eng
KW - degenerate operators in divergence form; Green's function
UR - http://eudml.org/doc/84032
ER -

References

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  1. [1] S. Chanillo - R.L. Wheeden, Weighted Poincaré and Sobolev inequalities and estimates for the Peano maximal functions, Amer. J. Math.107 (1985), pp. 1191-1226. Zbl0575.42026MR805809
  2. [2] S. Chanillo - R.L. Wheeden, Harnack's inequality and mean-value inequalities for solutions of degenerate elliptic equations, Comm. P.D.E.11 (10) (1986), pp. 1111-1134. Zbl0634.35035MR847996
  3. [3] E.B. Fabes - C.E. Kenig - R.P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. P.D.E.7 (1982), pp. 77-116. Zbl0498.35042MR643158
  4. [4] E.B. Fabes - D. Jerison - C. Kenig, The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 (1982), pp. 151-182. Zbl0488.35034MR688024
  5. [5] R. Gariepy - W.P. Ziemer, A regularity condition at the boundary for solutions of quasilinear elliptic equations, Arch. Rat. Mech. Analy.67 (1977-78), pp. 25-39. Zbl0389.35023MR492836
  6. [6] D. Gilbarg - N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag, 1983. Zbl0562.35001MR737190
  7. [7] M. Gruter - K.O. Widman, The Green function for uniformly elliptic equations, Manuscripta Math.37 (1982), pp. 303-342. Zbl0485.35031MR657523
  8. [8] D. Kinderlehrer - G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, 1980, New York. Zbl0457.35001MR567696
  9. [9] W. Littman - G. Stampacchia - H.F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. III17 (1963), pp. 43-77. Zbl0116.30302MR161019
  10. [10] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc.165 (1972), pp. 207-226. Zbl0236.26016MR293384
  11. [11] N.S. Trudinger, Linear elliptic operators with measurable coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. III, 27 (1973), pp. 275-308. Zbl0279.35025MR369884

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