Concentrated terms and varying domains in elliptic equations: Lipschitz case |
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| Authors: | Gleiciane S Aragão Simone M Bruschi |
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| Institution: | 1. Departamento de Ciências Exatas e da Terra, Universidade Federal de S?o Paulo. Rua Professor Artur Riedel, Diadema‐SP, Brazil;2. Departamento de Matemática, Universidade de Brasília. Campus Universitário Darcy Ribeiro, Brasília‐DF, Brazil |
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| Abstract: | 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 H1an 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 © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | semilinear elliptic equations nonlinear boundary value problems varying boundary oscillatory behavior concentrated terms upper semicontinuity of solutions |
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