Questions tagged [variational-inequalities]

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Estimate involving Besov norm

When reading some old notes of my advisor on interpolation spaces, I bumped into a problem I can't quite wrap my head around. Here are the details. For $p\in(0,\infty)$ a $p$-variation semi-norm of a ...
4
votes
1answer
122 views

Bound the operator norm of the Fréchet derivative of a Lipschitz function in this setting

I want to find a bound for the operator norm of the Fréchet derivative of a Lipschitz continuous function in the following setting: Let $E$ be a $\mathbb R$-Banach space; $v:E\to[1,\infty)$ be ...
2
votes
1answer
77 views

Explicit solution of a free boundary problem for heat equation

Consider the free boundary problem $$ \min\{u_t - u_{xx} -1, u \} = 0 \qquad \text{ in } (0,T)\times (-1,1) \\ u(0,\cdot) = 0 \qquad \text{ in } (-1,1)\\ u(\cdot, -1) = u(\cdot, 1) = 0 \qquad \...
2
votes
1answer
147 views

Numerical analysis of parabolic obstacle problem

I want to solve a parabolic obstacle problem, written as a variational inequality: For almost all $t\in [0,T]$ \begin{align*} \langle u'(t), v - u(t)\rangle +a(u(t),v-u(t)) \geq \langle f(t),v-u(t)\...