All Questions

Let $\Omega$ be a bounded domain in $\mathbb R^n$ with a smooth boundary and let $g$ be a smooth Riemannian metric on $\Omega$. Let $f_1,f_2,\ldots,f_n$ be non-constant smooth functions on $\partial \...

Let $\mathbb{D}^2$ be the closed two-dimensional unit disk, and let $g:\mathbb{D}^2 \to \mathbb{R}$ be a non-constant harmonic function (smooth up to the boundary). Does there exist a sequence of ...