Summability of the Solutions to Nonlinear Parabolic Equations with Measure Data

Feng-Quan Li; Guang-Wei Li

doi:10.68381/jca07011

Abstract

The authors improve the

L^p

estimates from the earlier papers of L. Boccardo, T. Gallouet, J. M. Rakotoson, et al., for weak solutions in

L^1(0, T; W_0^{1,1}(\Omega))

to nonlinear parabolic equations with right hand side and initial value involving measure data.We give an improvement of the summability of solutions to nonlinear parabolic equations with measure data.

Author information

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

Feng-Quan Li

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

Guang-Wei Li

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

Keywords

Summability
nonlinear parabolic equations
measure data

Mathematics Subject Classification

35D10; 35K60

References

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
J. M. Rakotoson: A compactness lemma for quasilinear problems: application to parabolic equations, J. Funct. Anal. 106 (1992) 358-374.https://doi.org/10.1016/0022-1236(92)90053-L Google Scholar
G. Dal Maso, F. Murat, L. Orsina, A. Prignet: Renormalized solutions of elliptic equations with general measure data, to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci.Google Scholar
L. Boccardo, T. Gallouët: Summability of the solutions of nonlinear elliptic equations with right hand side measures, J. Convex Anal. 3(2) (1996) 361-365.https://doi.org/10.68381/jca03024 Google Scholar
J. L. Lions: Quelques Méthodes de Résolution des Problémes aux Limites Nonlinéaires, Dunod, Paris, 1969.Google Scholar

Suggested citation

Published by Heldermann Verlag, 2000. Rights now held by Banach Press LLC.

[1] 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

[2] J. M. Rakotoson: A compactness lemma for quasilinear problems: application to parabolic equations, J. Funct. Anal. 106 (1992) 358-374.https://doi.org/10.1016/0022-1236(92)90053-L Google Scholar

[3] G. Dal Maso, F. Murat, L. Orsina, A. Prignet: Renormalized solutions of elliptic equations with general measure data, to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci.Google Scholar

[4] L. Boccardo, T. Gallouët: Summability of the solutions of nonlinear elliptic equations with right hand side measures, J. Convex Anal. 3(2) (1996) 361-365.https://doi.org/10.68381/jca03024 Google Scholar

[5] J. L. Lions: Quelques Méthodes de Résolution des Problémes aux Limites Nonlinéaires, Dunod, Paris, 1969.Google Scholar