Gradient bounds and Liouville theorems for quasilinear elliptic equations

L. A. Peletier; J. Serrin

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1978)

  • Volume: 5, Issue: 1, page 65-104
  • ISSN: 0391-173X

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Peletier, L. A., and Serrin, J.. "Gradient bounds and Liouville theorems for quasilinear elliptic equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.1 (1978): 65-104. <http://eudml.org/doc/83779>.

@article{Peletier1978,
author = {Peletier, L. A., Serrin, J.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {65-104},
publisher = {Scuola normale superiore},
title = {Gradient bounds and Liouville theorems for quasilinear elliptic equations},
url = {http://eudml.org/doc/83779},
volume = {5},
year = {1978},
}

TY - JOUR
AU - Peletier, L. A.
AU - Serrin, J.
TI - Gradient bounds and Liouville theorems for quasilinear elliptic equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1978
PB - Scuola normale superiore
VL - 5
IS - 1
SP - 65
EP - 104
LA - eng
UR - http://eudml.org/doc/83779
ER -

References

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  1. [1] E. Bohn - L.K. Jackson, The Liouville theorem for a quasilinear elliptic partial differential equation, Trans. Amer. Math. Soc., 104 (1962), pp. 392-397. Zbl0119.30704MR139840
  2. [2] R. Finn, Remarks relevant to minimal surfaces of constant mean curvature, J. d'Analyse Math., 14 (1965), pp. 139-160. Zbl0163.34604MR188909
  3. [3] D. Gilbarg - J.B. Serrin, On isolated singularities of solutions of second order elliptic differential equations, J. d'Analyse Math., 4 (1954-1956), pp. 165-174. Zbl0095.20804
  4. [4] A.V. Ivanov, Local estimates for the first derivatives of solutions of quasilinear elliptic equations and their applications to Liouville-type theorems, Sem. Steklov Inst. Leningrad, 30 (1972), pp. 40-50 (translation in J. Sov. Math., 1 (1973), pp. 416-430(. MR333429
  5. [5] M.H. Protter - H.F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1967. Zbl0153.13602MR219861
  6. [6] R.M. Redheffer, On the inequality Δu ≽ f(u, |grad u|), J. Math. Anal. Appl., 1 (1960), pp. 277-299. Zbl0116.07502
  7. [7] J. Serrin, Gradient estimates for nonlinear elliptic and parabolic partial differential equations, Symposium on Nonlinear Functional Analysis, University of Wisconsin Press (1972). Zbl0271.35004
  8. [8] J. Serrin, Entire solutions of nonlinear Poisson equations, Proc. London Math. Soc., 24 (1972), pp. 348-366. Zbl0229.35035MR289961
  9. [9] J. Serrin, Liouville theorems for quasilinear elliptic equations, Atti del Convegno Internazionale sui Metodi Valutativi nella Fisica-Matematica, Roma, Accademia Lincei, 1975. 
  10. [10] I.N. Tavgelidze, Liouville theorems for second order elliptic and parabolic equations, Vestnik Moskov Univ., 31 (1976), pp. 28-35. Zbl0341.35032MR430492

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