A new approach to initial traces in nonlinear filtration

Abstract

For weak solutions of equations of the type of nonlinear filtration in RN × (0, T), 0 < T < ∞, we prove precise sup-estimates and local and global Harnack type inequalities. These estimations permit to identify the initial traces and describe the behavior of such solutions as |x| → ∞.The main point is to introduce a new approach, free of the specific features of the porous medium equation such as homogeneity, scaling, quasi-convexity, etc. This approach on one hand allows generalizations to a large variety of equations and on other yields new results on gradient averages.