An Obstacle Problem for Nonlocal Equations in Perforated Domains

Author(s)

Pereira, Marcone C. ^[1] ; Rossi, Julio D. ^[2]

Affiliation

^[1] Univ Sao Paulo, IME, Dept Matemat Aplicada, Rua Matao 1010, Sao Paulo, SP - Brazil

^[2] Univ Buenos Aires, Dept Matemat, FCEyN, Ciudad Univ Pab 1, RA-1428 Buenos Aires, DF - Argentina

• Document type: Journal article
• Source: POTENTIAL ANALYSIS; v. 48, n. 3, p. 361-373, APR 2018.
• Web of Science Citations: 2

Abstract

In this paper we analyze the behavior of solutions to a nonlocal equation of the form J au u (x) - u (x) = f (x) in a perforated domain Omega a- A (oee-) with u = 0 in and an obstacle constraint, u > psi in Omega a- A (oee-) . We show that, assuming that the characteristic function of the domain Omega a- A (oee-) verifies weakly (au) in , there exists a weak limit of the solutions u (oee-) and we find the limit problem that is satisfied in the limit. When in this limit problem an extra term appears in the equation as well as a modification of the obstacle constraint inside the domain. (AU)

• FAPESP's process: 15/17702-3 - Obstacle problems for non local evolution equations
• Grantee: Marcone Corrêa Pereira
• Support Opportunities: Scholarships abroad - Research