Journal of Convex Analysis 07 (2000), No. 2, 353--374
Copyright Heldermann Verlag 2000
Homographic Approximation for Some Nonlinear Parabolic Unilateral Problems
Maria Carla Palmeri
Dip. di Matematica, UniversitÓ di Roma 1, Piazzale A. Moro 5, 00185 Roma, Italy
We deal with nonlinear parabolic unilateral problems by means of the homographic approximation, introduced by C. M. Brauner and B. Nicolaenko [in: "Nonlinear Partial Diff. Equations and Their Applications", H. Brezis, J. L. Lions (eds.), Research Notes in Mathematics 70 (1982) 86--128] in the linear elliptic case. The interest in this kind of penalty method arises from the fact that, in contrast with the usual penalization the homographic approximation is a "bounded penalty", which turns out to be convenient to have a priori estimates on the approximate solutions.
We present two different situations in which the homographic approximation gives advantages to solve evolutionary unilateral problems. First, in a variational framework, we are interested in strong solutions to nonlinear parabolic variational inequalities; then, in a second case, we consider obstacle problems with L1 data.
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