A. Ponce

activity

20062025

most citedDiffuse measures and nonlinear parabolic equations

70 citations · 257 across the 32 of their papers we have counts for

collaborators

Showing 2012 · math.APShow all

4 papers · 2 filters

math.AP2012

Limit solutions of the Chern-Simons equation

Augusto C. Ponce, Adilson E. Presoto

We investigate the scalar Chern-Simons equation $- Δ u + e^{u} (e^{u} - 1) = μ$ in cases where there is no solution for a given nonnegative finite measure $μ$ . Approximating $μ$ by a sequen…

math.AP2012

Flat solutions of the 1-Laplacian equation

Luigi Orsina, Augusto C. Ponce

For every $f \in L^{N} (Ω)$ defined in an open bounded subset $Ω$ of $R^{N}$ , we prove that a solution $u \in W_{0}^{1, 1} (Ω)$ of the $1$ -Laplacian equation ${-}\mathrm{div}{(\fr…

math.AP2012★ 3 cited

Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates

Augusto C. Ponce

We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N…

math.AP2012★ 23 cited

Selected problems on elliptic equations involving measures

Augusto C. Ponce

This monograph is the core of my book "Elliptic PDEs, Measures and Capacities: From the Poisson equation to Nonlinear Thomas-Fermi Problems" which has received the 2014 EMS Monogra…