Concentrated terms and varying domains in elliptic equations: Lipschitz case

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2016
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Aragao, Gleiciane S. [UNIFESP]
Bruschi, Simone M.
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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.
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Mathematical Methods In The Applied Sciences. Hoboken, v. 39, n. 12, p. 3450-3460, 2016.
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