A. Gachechiladze
Abstract:
The existence and uniqueness problems for some quasi-variational inequalities
are studied on the basis of the L∞-estimates
for solutions of the variational inequalities and their differences. An implicit
obstacle problem is stated by analogy with one quasi-variational inequality
studied by Benoussan and Lions (1982) and Vescan (1982) and its unique
solvability is proved. Some conclusions are given concerning the uniqueness of
solutions for an impulse control problem with bilateral restrictions and for a
quasi-variational inequality appearing in dynamic programming.
Keywords:
Variational and quasi-variational inequalities, impulse control, dynamic
programming, implicit Signorini problem
MSC 2000: 35J85, 35B50, 58E35, 49J40, 49N25.