Let $V \subset H \subset V^*$ be a Gelfand triple of Hilbert spaces. Take $f,\psi \in L^2(0,T;H)$ and consider the VI: find $u \in L^2(0,T;V)$ with $u' \in L^2(0,T;V^*)$ such that

$$u(t) \leq \psi(t) : \int_0^T \langle u' + Au - f, v-u \rangle \geq 0\quad \forall v \in L^2(0,T;V) : v(t) \leq \psi(t).$$

$A$ is some smooth elliptic operator.

Can I expect $u' \in L^2(0,T;H)$, at least with additional assumptions? Could anyone refer me to a reference for this? The only literature is see has the obstacle $\psi$ independent of time, which is not the case here.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.