70 citations · 257 across the 32 of their papers we have counts for
7 papers · 1 filter
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…
A note on the fractional perimeter and interpolation
Augusto C. Ponce, Daniel Spector
We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fracti…
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,\\…
A Boxing Inequality for the Fractional Perimeter
Augusto C. Ponce, Daniel Spector
We prove the Boxing inequality: for every $α\in…
Gauge-measurable functions
Augusto C. Ponce, Jean Van Schaftingen
In 1973, E.J. McShane proposed an alternative definition of the Lebesgue integral based on Riemann sums, where gauges are used decide what tagged partitions are allowed. Such an ap…
Hopf potentials for the Schrödinger operator
Luigi Orsina, Augusto C. Ponce
We establish the Hopf boundary point lemma for the Schrödinger operator involving potentials that merely belong to the space . More precisely, we prove…