Parabolic Q-minima and Their Application

Abstract

In this paper, the notion named parabolic Q-minima is endowed with rich meanings and its local behavior is investigated. As its direct application we obtain the local regularity, such as boundcdncss, continuity, llolder continuity of the weak solutions of the various filtration equations, e.g., the equation of Newtonian polytropic filtration, the general equation of Newtonian filtration, the equation of elastic filtration, the equation of non-Newtonian polytropic filtration. Therefore, a unifying approach to various regularity results for a great number of nonlinear degenerate parabolic equations is provided.