All Questions

$\DeclareMathOperator\diam{diam}$Looking for a proof in the literature of the following lemma: Let $K\subset\mathbb{R}^d$ be a bounded domain. Let $P_X$ be a finite dimensional subspace of $\mathcal{...

I am investigating the following standard elliptic PDE with mixed Dirichlet-Neumann boundary condition: $-\Delta u=f$ on $\Omega$; $u=0$ on $\Gamma_D$; $\left<n,\nabla u=g\right>$ on $\Gamma_N$ ...

I am interested in some sort of analytic interpolation. A toy version of my problem is as follows. Let $V \subset \mathbb{C}$ be a complex neighborhood of $[0,1]$. Assume there is some bounded ...

I encountered a problem working through a paper about modeling flow with the use of the Poisson equation (source given below). There appears an inequality of L2 norms I don't understand so far. Your ...

Let $\mathcal{H}=(H^1(\mathbb{R}^3))^N$ be the product space with the associated norm $$ \Vert U\Vert_1=\left(\sum^N_{i=1}\Vert u_i\Vert_1^2\right)^{1/2} $$ where $U=(u_1,u_2,...,u_N)\in\mathcal{H}$. ...