Concentrated terms and varying domains in elliptic equations: Lipschitz case

Date
2016Author
Aragao, Gleiciane S. [UNIFESP]
Bruschi, Simone M.
Type
ArtigoISSN
0170-4214Is part of
Mathematical Methods In The Applied SciencesDOI
10.1002/mma.3791Metadata
Show full item recordAbstract
In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior, which is uniformly Lipschitz and nonlinear terms, are concentrated in a region, which neighbors the boundary of domain. We prove that this family of solutions converges to the solutions of a limit problem in H(1)an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.Copyright (c) 2015 John Wiley & Sons, Ltd.
Citation
Mathematical Methods In The Applied Sciences. Hoboken, v. 39, n. 12, p. 3450-3460, 2016.Keywords
semilinear elliptic equationsnonlinear boundary value problems
varying boundary
oscillatory behavior
concentrated terms
upper semicontinuity of solutions
Sponsorship
CNPq, BrazilFEMAT-Brazil
Collections
- ICAQF - Artigos [1056]