Concentrated terms and varying domains in elliptic equations: Lipschitz case | Zendy

Aragão Gleiciane S. | Zendy; Bruschi Simone M. | Zendy

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Concentrated terms and varying domains in elliptic equations: Lipschitz case

Author(s) -

Aragão Gleiciane S.,

Bruschi Simone M.

Publication year - 2016

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.3791

Subject(s) - mathematics , lipschitz continuity , nonlinear system , boundary (topology) , mathematical analysis , domain (mathematical analysis) , lipschitz domain , boundary value problem , elliptic curve , limit (mathematics) , physics , quantum mechanics

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 © 2015 John Wiley & Sons, Ltd.

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