Anisotropic Elliptic Equations in L^m

Feng-Quan Li

doi:10.68381/jca08022

Abstract

We prove the existence of solutions to anisotropic nonlinear elliptic equations with right hand side term in

L^m(\Omega)

and obtain the appropriate function space for the weak solutions. This paper gives a generalization of some results given by L. Boccardo, T. Gallouet and P. Marcellini [Diff. Integral Equations 9 (1996) 209–212] and by L. Boccardo and T. Gallouet [Comm. Partial Diff. Equations 17 (1992) 641–655].

Author information

Contact details are reproduced from the original publication and may be historical.

Feng-Quan Li

Dept. of Mathematics, Qufu Normal University, Qufu 273165, Shandong, P. R. China

Keywords

Anisotropic elliptic equations
Lm data

Mathematics Subject Classification

35D05; 35D10, 35J65

References

L. Boccardo, T. Gallouët, P. Marcellini: Anisotropic equations in L1, Differential and Integral Equations 9(1) (1996) 209–212.https://doi.org/10.57262/die/1367969997 Google Scholar
L. Boccardo, T. Gallouët: Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989) 149–169.https://doi.org/10.1016/0022-1236(89)90005-0 Google Scholar
L. Boccardo, T. Gallouët: Nonlinear elliptic equations with right hand side measures, Comm. Partial Differential Equations 17(3-4) (1992) 641–655.https://doi.org/10.1080/03605309208820857 Google Scholar
J. L. Lions: Quelques Méthodes de Résolution des Problémes aux Limites Nonlinéaires, Dunod, Paris, 1968.Google Scholar
M. Troisi: Theoremi di inclusione per spazi di Sobolev nonisotropi, Ricerche Mat. 18 (1969) 3–24.Google Scholar
L. Boccardo, T. Gallouét, J. L. Vazquez: Nonlinear elliptic equations in RN without growth restrictions on the data, J. Differential Equations 105 (1993) 334–363.https://doi.org/10.1006/jdeq.1993.1092 Google Scholar

Suggested citation

Published by Heldermann Verlag, 2001. Rights now held by Banach Press LLC.

[1] L. Boccardo, T. Gallouët, P. Marcellini: Anisotropic equations in L1, Differential and Integral Equations 9(1) (1996) 209–212.https://doi.org/10.57262/die/1367969997 Google Scholar

[2] L. Boccardo, T. Gallouët: Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989) 149–169.https://doi.org/10.1016/0022-1236(89)90005-0 Google Scholar

[3] L. Boccardo, T. Gallouët: Nonlinear elliptic equations with right hand side measures, Comm. Partial Differential Equations 17(3-4) (1992) 641–655.https://doi.org/10.1080/03605309208820857 Google Scholar

[4] J. L. Lions: Quelques Méthodes de Résolution des Problémes aux Limites Nonlinéaires, Dunod, Paris, 1968.Google Scholar

[5] M. Troisi: Theoremi di inclusione per spazi di Sobolev nonisotropi, Ricerche Mat. 18 (1969) 3–24.Google Scholar

[6] L. Boccardo, T. Gallouét, J. L. Vazquez: Nonlinear elliptic equations in RN without growth restrictions on the data, J. Differential Equations 105 (1993) 334–363.https://doi.org/10.1006/jdeq.1993.1092 Google Scholar