Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

dc.contributorUniversidade Estadual Paulista (UNESP)
dc.creatorArrieta, Jose M.
dc.creatorBruschi, Simone M.
dc.date2014-02-26T17:01:46Z
dc.date2014-05-20T14:17:03Z
dc.date2016-10-25T17:39:46Z
dc.date2014-02-26T17:01:46Z
dc.date2014-05-20T14:17:03Z
dc.date2016-10-25T17:39:46Z
dc.date2007-10-01
dc.date.accessioned2017-04-05T22:23:36Z
dc.date.available2017-04-05T22:23:36Z
dc.identifierMathematical Models & Methods In Applied Sciences. Singapore: World Scientific Publ Co Pte Ltd, v. 17, n. 10, p. 1555-1585, 2007.
dc.identifier0218-2025
dc.identifierhttp://hdl.handle.net/11449/25108
dc.identifierhttp://acervodigital.unesp.br/handle/11449/25108
dc.identifier10.1142/S0218202507002388
dc.identifierWOS:000251742500004
dc.identifierhttp://dx.doi.org/10.1142/S0218202507002388
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/870037
dc.descriptionWe analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.
dc.languageeng
dc.publisherWorld Scientific Publ Co Pte Ltd
dc.relationMathematical Models & Methods In Applied Sciences
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectvarying boundary
dc.subjectoscillations
dc.subjectnonlinear boundary conditions
dc.subjectelliptic equations
dc.titleRapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation
dc.typeOtro


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