Well-posedness and qualitative properties for nonlinear PDEs
Regularity estimates for fully nonlinear ellpitic models with oblique boundary con...
Systems of partial differential equations and nonlinear elliptic equations
| Full text | |
| Author(s): |
Arrieta, Jose M.
;
Nogueira, Ariadne
;
Pereira, Marcone C.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 24, n. 8, p. 30-pg., 2019-08-01. |
| Abstract | |
In this paper we analyze the asymptotic behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating region with reaction terms concentrated in a neighborhood of the oscillatory boundary theta(epsilon) subset of Omega(epsilon) subset of R-2 when a small parameter epsilon > 0 goes to zero. Our main result is concerned with the upper and lower semicontinuity of the set of solutions in H-1. We show that the solutions of our perturbed equation can be approximated with one defined in a fixed limit domain, which also captures the effects of reaction terms that take place in the original problem as a flux condition on the boundary of the limit domain. (AU) | |
| FAPESP's process: | 17/02630-2 - Asymptotic analysis in differential and integral equations |
| Grantee: | Marcone Corrêa Pereira |
| Support Opportunities: | Regular Research Grants |