Nonlinear degenerate elliptic equations with measure data

Fengquan Li

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 4, page 647-658
  • ISSN: 0010-2628

Abstract

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In this paper we prove existence results for some nonlinear degenerate elliptic equations with data in the space of bounded Radon measures and we improve the results already obtained in Cirmi G.R., On the existence of solutions to non-linear degenerate elliptic equations with measure data, Ricerche Mat. 42 (1993), no. 2, 315–329.

How to cite

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Li, Fengquan. "Nonlinear degenerate elliptic equations with measure data." Commentationes Mathematicae Universitatis Carolinae 48.4 (2007): 647-658. <http://eudml.org/doc/250234>.

@article{Li2007,
abstract = {In this paper we prove existence results for some nonlinear degenerate elliptic equations with data in the space of bounded Radon measures and we improve the results already obtained in Cirmi G.R., On the existence of solutions to non-linear degenerate elliptic equations with measure data, Ricerche Mat. 42 (1993), no. 2, 315–329.},
author = {Li, Fengquan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonlinear degenerate elliptic equations; existence; measure data; nonlinear degenerate elliptic equations; existence; measure data},
language = {eng},
number = {4},
pages = {647-658},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Nonlinear degenerate elliptic equations with measure data},
url = {http://eudml.org/doc/250234},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Li, Fengquan
TI - Nonlinear degenerate elliptic equations with measure data
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 4
SP - 647
EP - 658
AB - In this paper we prove existence results for some nonlinear degenerate elliptic equations with data in the space of bounded Radon measures and we improve the results already obtained in Cirmi G.R., On the existence of solutions to non-linear degenerate elliptic equations with measure data, Ricerche Mat. 42 (1993), no. 2, 315–329.
LA - eng
KW - nonlinear degenerate elliptic equations; existence; measure data; nonlinear degenerate elliptic equations; existence; measure data
UR - http://eudml.org/doc/250234
ER -

References

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  2. Boccardo L., Gallouët T., Nonlinear elliptic equations with right hand side measures, Comm. Partial Differential Equations 17 3-4 (1992), 641-655. (1992) MR1163440
  3. Rakotoson J.M., Quasilinear elliptic problems with measure as data, Differential Integral Equations 4 (1991), 449-457. (1991) MR1097910
  4. Rakotoson J.M., Generalized solutions in a new type of sets for problems with measures as data, Differential Integral Equations 6 1 (1993), 27-36. (1993) Zbl0780.35047MR1190163
  5. Bénilan Ph., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vazquez J.L., An L 1 -theory of existence and uniqueness of solutions of non-linear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22 2 (1995), 241-273. (1995) MR1354907
  6. Dal Maso G., Murat F., Orsina L., Prignet A., Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4) 28 4 (1999), 741-808. (1999) MR1760541
  7. Cirmi G.R., On the existence of solutions to non-linear degenerate elliptic equations with measure data, Ricerche Mat. 42 2 (1993), 315-329. (1993) MR1283363
  8. Rakotoson J.M., Resolution of the critical cases for problems with L 1 data, Asymptotic Analysis 6 (1993), 285-293. (1993) MR1201197
  9. Heinonen J., Kilpeläinen T., Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1993. MR1207810
  10. Murthy M.K.V., Stampacchia G., Boundary value problems for some degenerate elliptic operators, Ann. Mat. Pura Appl. 90 (1971), 1-122. (1971) Zbl0226.35037MR0249828
  11. Leray J., Lions J.L., Quelques résultats de Višik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty et Browder, Bull. Soc. Math. France 93 (1965), 97-107. (1965) MR0194733
  12. Lions J.L., Quelques méthodes de résolution des problèmes aux limites nonlinéaires, Dunod, Paris, 1969. 
  13. Porretta A., Some remarks on the regularity of solutions for a class of elliptic equations with measure data, Houston. J. Math. 26 1 (2000), 183-213. (2000) Zbl0974.35032MR1814734
  14. Li F.Q., Nonlinear degenerate parabolic equations with measure data, Nonlinear Anal. 61 (2005), 1269-1282. (2005) Zbl1073.35133MR2131654

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