Estimates on the Support of Solutions of Parabolic Variational Inequalities


and of (1.2), the situation is entirely different: when f is uniformly negative, u(x, t) has compact support whenever uo(x) has compact support. The object of this paper is to study properties of the support. In Section 2 we study the variational inequality (1.3), (1.2) when uo is any finite measure. Existence and uniqueness are proved. In Sections 3-6 it is assumed that f is bounded and is uniformly negative. In Section 3 we show that if uo(x) has compact support then u(x, t) has compact support. An analogous result for elliptic variational inequalities was proved earlier by Br6zis [2] (and then generalized by Redheffer [6]). In Sections 4 and 5 we study the behavior of the support S(t) of the function x u(x, t). In Section 4 we consider the case where uo is any function in L(R") with compact support S S(0); thus uo is not required to vanish on OS. It is proved that, for all small times t,

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@inproceedings{BrizisEstimatesOT, title={Estimates on the Support of Solutions of Parabolic Variational Inequalities}, author={Haim Brizis and Avner Friedman} }