## View abstract

### Session S02 - Diverse Aspects of Elliptic PDEs and Related Problems

Thursday, July 15, 19:00 ~ 19:30 UTC-3

## Obstacle type problems with gradient constrains.

### Héctor Chang-Lara

#### Centro de Investigación en Matemáticas - Guanajuato, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak458f410c370f7906d623c8ef048b560c').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy458f410c370f7906d623c8ef048b560c = 'h&#101;ct&#111;r.ch&#97;ng' + '&#64;'; addy458f410c370f7906d623c8ef048b560c = addy458f410c370f7906d623c8ef048b560c + 'c&#105;m&#97;t' + '&#46;' + 'mx'; var addy_text458f410c370f7906d623c8ef048b560c = 'h&#101;ct&#111;r.ch&#97;ng' + '&#64;' + 'c&#105;m&#97;t' + '&#46;' + 'mx';document.getElementById('cloak458f410c370f7906d623c8ef048b560c').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy458f410c370f7906d623c8ef048b560c + '\'>'+addy_text458f410c370f7906d623c8ef048b560c+'<\/a>';

We study the regularity of solutions of equations of the form $\min(-\Delta u,|Du|−1)=0$ These arise when computing the optimal strategy for a zero-sum game involving Brownian and constant speed dynamics determined by the agents. In collaboration with Pimentel we established the optimal Lipschitz regularity and the free boundary condition on the interface. Whenever the first agent fixes its strategy the equation becomes a transmission problem between the Laplace and eikonal equation. In different collaboration with Arellano we analyze the well posedness of the problem and the convergence of a numerical method.

Joint work with Edgard Pimentel (Pontifícia Universidade Católica do Rio de Janeiro, Brasil) and Arturo Arellano (Centro de Investigación en Matemáticas, Guanajuato, México).