International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 27, Pages 1725-1730
On a nonlinear compactness lemma in
Laboratoire de Modélisation et Calcul, Université Joseph Fourier, BP 53, Grenoble Cedex 9 38041, France
Received 20 June 2001; Revised 2 February 2002
Copyright © 2003 Emmanuel Maitre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a nonlinear counterpart of a compactness lemma of
Simon (1987), which arises naturally in the study of doubly
nonlinear equations of elliptic-parabolic type. This
paper was motivated by previous results of Simon (1987), recently
sharpened by Amann (2000), in the linear setting, and by a
nonlinear compactness argument of Alt and Luckhaus (1983).