Boundary oscillations and nonlinear boundary conditions
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2006-07-15
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Elsevier B.V.
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We study how oscillations in the boundary of a domain affect the behavior of solutions of elliptic equations with nonlinear boundary conditions of the type partial derivative u/partial derivative n + g(x, u) = 0. We show that there exists a function gamma defined on the boundary, that depends on an the oscillations at the boundary, such that, if gamma is a bounded function, then, for all nonlinearities g, the limiting boundary condition is given by partial derivative u/partial derivative n + gamma(x)g(x, u) = 0 (Theorem 2.1, Case 1). Moreover, if g is dissipative and gamma infinity then we obtain a Dirichlet an boundary condition (Theorem 2.1, Case 2).
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Comptes Rendus Mathematique. Paris: Elsevier France-editions Scientifiques Medicales Elsevier, v. 343, n. 2, p. 99-104, 2006.
