This is the fourth and last part of the special issue in the Bulletin dedicated to Prof. Trudinger on the occasion of his 70th birthday. The editors of this special issue would like to take this opportunity to thank all the authors again for their contributions.

Sun-Yung Alice Chang, Department of Mathematics, Princeton University, U. S. A.

Nicola Fusco, Dipartimento di Matematica “R. Caccioppoli",, Universita di Napoli "Federico II", Italy

Tai-Ping Liu, Institute of Mathematics, Academia Sinica, Taiwan, and Department of Mathematics, Stanford University, U.S.A. .

Alan McIntosh, Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Australia