Electronic Journal of Differential Equations, Vol. 2003(2003), No. 10, pp. 1-13. Title: Some integral inequalities for functions of two variables Authors: Sever S. Dragomir (Victoria Univ. of Technology, Australia) Young-Ho Kim (Changwon National Univ., Korea) Abstract: In this article, we establish some integral inequalities for function with two independent variables. Also we show applications of these inequalities for finding bounds of solutions to partial differential equations. Submitted April 19, 2002. Published February 4, 2003. Math Subject Classifications: 26D10, 26D15. Key Words: Integral inequality; partial differential equations.