On a regularity property and a priori estimates for solutions of nonlinear parabolic variational inequalities

Haruo Nagase
2000 Nagoya mathematical journal  
AbstractIn this paper we consider the following nonlinear parabolic variational inequality;u(t) ∈D(Φ) for allwhere Δpis the so-called p-Laplace operator and Φ is a proper, lower semicontinuous functional. We have obtained two results concerning to solutions of this problem. Firstly, we prove a few regularity properties of solutions. Secondly, we show the continuous dependence of solutions on given datau0andf.
doi:10.1017/s0027763000007716 fatcat:5ots67onn5b7fjm5rp3wik7osy