Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions

Guy Barles; Alain-Philippe Blanc; Christine Georgelin; Magdalena Kobylanski

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1999)

  • Volume: 28, Issue: 3, page 381-404
  • ISSN: 0391-173X

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Barles, Guy, et al. "Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 28.3 (1999): 381-404. <http://eudml.org/doc/84382>.

@article{Barles1999,
author = {Barles, Guy, Blanc, Alain-Philippe, Georgelin, Christine, Kobylanski, Magdalena},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {nonlinear elliptic PDE; maximum principle; quadratic growth condition},
language = {eng},
number = {3},
pages = {381-404},
publisher = {Scuola normale superiore},
title = {Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions},
url = {http://eudml.org/doc/84382},
volume = {28},
year = {1999},
}

TY - JOUR
AU - Barles, Guy
AU - Blanc, Alain-Philippe
AU - Georgelin, Christine
AU - Kobylanski, Magdalena
TI - Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1999
PB - Scuola normale superiore
VL - 28
IS - 3
SP - 381
EP - 404
LA - eng
KW - nonlinear elliptic PDE; maximum principle; quadratic growth condition
UR - http://eudml.org/doc/84382
ER -

References

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  1. [1] G. Barles - F. Murat, The Maximum Principle for quasilinear elliptic equations with quadratic growth conditions, Arch. Rational Mech. Anal.133 (1995), 77-101. Zbl0859.35031MR1367357
  2. [2] A. Bensoussan - L. Boccardo - F. Murat, On a nonlinear partial differential equation having natural growth terms and unbounded solution, Ann. Inst. H. Poincaré, Anal. Non Linéaire5 (1988), 347-364. Zbl0696.35042MR963104
  3. [3] L. Boccardo - F. Murat - J.P. Puel, Existence de solutions non bornées pour certaines équations quasi-linéaires, Portugal. Math.41 (1982), 507-534. Zbl0524.35041MR766873
  4. [4] L. Boccardo - F. Murat - J.-P. Puel, Existence de solutions faibles pour des équations elleptiques quasi-linéaires à croissance quadratique, In: "Nonlinear Partial Differential and their Applications", Collège de France Seminar, volume IV, H. Brezis and J.-L. Lions editors, Research Notes in Mathematics84, Pitman, London, 1983, pp. 19-73. Zbl0588.35041MR716511
  5. [5] V. Ferone - F. Murat, Nonlinear problems having natural growth in the gradient: an existence result when the source term is small, Nonlinear Anal., to appear. Zbl1158.35358MR1780731
  6. [6] V. Ferone - F. Murat, Quasilinear problems having natural growth in the gradient: an existence result when the source term is small, In: "Equations aux dérivées partielles et applications, article dédié à Jacques-Louis Lions", Gauthier-Villars, Paris, 1998, pp. 497-515. Zbl0917.35039MR1648236
  7. [7] V. Ferone - M.R. Posteraro, On a class of quasilinear elliptic equations with quadratic growth in the gradient, Nonlinear Anal.20 (1993). Zbl0801.35028MR1214736
  8. [8] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer-Verlag, Berlin, 1977. Zbl0361.35003MR473443
  9. [9] J.L. Kazdan - R.J. Kramer, Invariant criteria for existence of solutions of second order quasi-linear elliptic equations, Comm. Pure Appl. Math.31 (1978), 619-645. Zbl0368.35031MR477446
  10. [10] O.A. Lady - N.N. Ural'ceva, "Équations aux derivées partielles de type elliptique, Dunod, Paris, 1968. Zbl0164.13001MR239273
  11. [11] J.M. Lasry - P.L. Lions, A remark on regularization in Hilbert spaces, Isr. J. Math. 55 (1986), 257-266. Zbl0631.49018MR876394

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