70 citations · 257 across the 32 of their papers we have counts for
18 papers · 1 filter
Diffuse measures and nonlinear parabolic equations
Francesco Petitta, Augusto C. Ponce, Alessio Porretta
Given a parabolic cylinder , where is a bounded domain, we prove new properties of solutions of \[ u_t-Δ_p u = μ\quad \text{in } \] wi…
An Agmon-Allegretto-Piepenbrink principle for Schroedinger operators
Stefano Buccheri, Luigi Orsina, Augusto C. Ponce
We prove that each Borel function defined on an open subset induces a decomposition such that…
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 $…
On the nonexistence of Green's function and failure of the strong maximum principle
Luigi Orsina, Augusto C. Ponce
Given any Borel function on a smooth bounded domain , we establish that the strong maximum principle for the Schrödinger operator $…
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…