Continuity of Weak Solutions for Quasilinear Parabolic Equations with Strong Degeneracy*

Abstract

The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form

u _t − Δ∅(u) = 0,

where ∅ ∈ C ¹(ℝ¹) is a strictly monotone increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of ∅'( · ) is permitted to have zero measure. This is an answer to an open problem in [13, p. 288].

Keywords

Continuity of weak solutions / Quasilinear degenerate parabolic equation / 35L80 / 35L60 / 35L15 / 35B40 / 35F25

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