Abstract

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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Maria Carla Palmeri

Dip. di Matematica, Università di Roma 1, Piazzale A. Moro 5, 00185 Roma, Italy

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Suggested citation

M. C. Palmeri. “Homographic Approximation for Some Nonlinear Parabolic Unilateral Problems.” Journal of Convex Analysis 7 (2000), No. 2, 353–373. https://doi.org/10.68381/jca07018

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Published by Heldermann Verlag, 2000. Rights now held by Banach Press LLC.