11 citations · 17 across the 4 of their papers we have counts for
4 papers
A representation formula for the distributional normal derivative
Augusto C. Ponce, Nicolas Wilmet
We prove an integral representation formula for the distributional normal derivative of solutions of $$ \left\{ \begin{aligned} - Δu + V u &= μ&& \text{in ,}\\ u &= 0 && \text{o…
The Hopf lemma for the Schrödinger operator
Augusto C. Ponce, Nicolas Wilmet
We prove the Hopf boundary point lemma for solutions of the Dirichlet problem involving the Schrödinger operator with a nonnegative potential which merely belongs to $…
Optimal control of nonlinear elliptic problems with sparsity
Augusto C. Ponce, Nicolas Wilmet
We study the minimization of the cost functional \[ F(μ) = \lVert u - u_d \rVert_{L^p(Ω)} + α\lVert μ\rVert_{\mathcal{M}(Ω)}, \] where the controls are taken in the space of fi…
Schroedinger operators involving singular potentials and measure data
Augusto C. Ponce, Nicolas Wilmet
We study the existence of solutions of the Dirichlet problem for the Schroedinger operator with measure data $$ \left\{ \begin{alignedat}{2} -Δu + Vu & = μ&& \quad \text{in } Ω,\\…