The obstacle problem for functions of least gradient
The obstacle problem for functions of least gradient
For a given domain $\Omega\subset\Bbb{R}^n$, we consider the variational problem of minimizing the $L^1$-norm of the gradient on $\Omega$ of a function $u$ with prescribed continuous boundary values and satisfying a continuous lower obstacle condition $u\ge\psi$ inside $\Omega$. Under the assumption of strictly positive mean curvature of the boundary $\partial\Omega$, …