Local Partial Regularity Theorems for Suitable Weak Solutions of a Class of Degenerate Systems

摘要

A partial regularity theorem is established for a particular class of weak solutions to the system au/at- div(K(u) ▽u) = σ(u)|▽Ψ|~2, div(σ(u) ▽Ψ) =0 on a bounded domain in R~N. Under our assumptions, σ(u) may exhibit exponential decay, and thus the system may be degenerate. Our proof is based upon a blow-up argument.