Gleiciane da Silva Aragao, Simone Mazzini Bruschi
Abstract:
In this article, we analyze the limit of the solutions of nonlinear
elliptic equations with Neumann boundary conditions, when nonlinear terms
are concentrated in a region which neighbors the boundary of domain and
this boundary presents a highly oscillatory behavior which is non
uniformly Lipschitz. More precisely, if the Neumann boundary conditions
are nonlinear and the nonlinearity in the boundary is dissipative, then we
obtain a limit equation with homogeneous Dirichlet boundary conditions.
Moreover, if the Neumann boundary conditions are homogeneous, then we obtain
a limit equation with nonlinear Neumann boundary conditions, which captures
the behavior of the concentration's region. We also prove the upper
semicontinuity of the families of solutions for both cases.
Submitted February 28, 2015. Published August 19, 2015.
Math Subject Classifications: 35J60, 30E25, 35B20, 35B27.
Key Words: Nonlinear elliptic equation; boundary value problem;
varying boundary; oscillatory behavior; concentrating term;
upper semicontinuity.
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Gleiciane da Silva Aragão Departamento de Ciências Exatas e da Terra Universidade Federal de São Paulo Rua Professor Artur Riedel, 275, Jardim Eldorado Cep 09972-270, Diadema-SP, Brazil email: gleiciane.aragao@unifesp.br, Phone (+55 11) 33193300 |
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Simone Mazzini Bruschi Departamento de Matemática Universidade de Brasília Campus Universitário Darcy Ribeiro ICC Centro, Bloco A, Asa Norte Cep 70910-900, Brasília-DF, Brazil email: sbruschi@unb.br, Phone (+55 61) 31076389 |
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