In a career of nearly sixty years of mathematical research, Guangchang Dong’s influence on the development of partial differential equations in China has been immense, at both teaching and research levels. To celebrate Prof. Dong’s eightieth birthday, an international conference called Elliptic and Parabolic Equations and Applications was held in August 2008 at Zhejiang University in Hangzhou, China. This volume presents fifteen papers in all – some drawn from lectures given at the conference, others by his friends and former students. Table of Contents: Viscosity Solutions of Bellman Equations Arising in Pricing Passport Options - Baojun Bian and Yang Wang; On Global Partial Regularity for Borderline Solutions of Semilinear Parabolic Problems - Kai-Seng Chou and Shi-Zhong Du; The Dirichlet Problem for Complex Monge-Ampère Equations and Applications - Bo Guan; Some Recent Works on Multiparameter Hardy Space Theory and Discrete Littlewood-Paley Analysis - Yongsheng Han and Guozhen Lu; Some Analytic Aspects of Liquid Crystal Configurations - Min-Chun Hong; Extremal Sub-manifolds in Minkowski Space-time - De-Xing Kong; Bounds of Eigenvalues on Riemannian Manifolds - Jun Ling and Zhiqin Lu; Wave Breaking Phenomena and Stability of Peakons for the Degasperis-Procesi Equation - Yue Liu; The Convexity of Level Sets for Solutions to Partial Differential Equations - Xi-Nan Ma and Qianzhong Ou; Nucleation of Instability of Meissner State of Superconductors and Related Mathematical Problems - Xing-Bin Pan; Calculus of Some Geometric Variations in Finsler Geometry - Yi-Bing Shen; Regularity and Singularity in the Mean Curvature Flow - Weimin Sheng and Xu-Jia Wang; Study of Finite Point Method - Longjun Shen and Guixia Lv; Nonlinear Diffusion Equations with Different Kind of Degeneracy - Jingxue Yin, Peidong Lei and Chunpeng Wang; Canonical Metrics on Toric Manifolds - Xiaohua Zhu; List of publications by Guangchang Dong