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Dive into the research topics where Carmen Perugia is active.

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Featured researches published by Carmen Perugia.


Mathematische Nachrichten | 2010

A gap in the essential spectrum of a cylindrical waveguide with a periodic aperturbation of the surface

Giuseppe Cardone; Sergey A. Nazarov; Carmen Perugia

It is proved that small periodic singular perturbation of a cylindrical waveguide surface may open a gap in the continuous spectrum of the Dirichlet problem for the Laplace operator. If the perturbation period is long and the caverns in the cylinder are small, the gap certainly opens.


Journal of Differential Equations | 2013

Uniform resolvent convergence for strip with fast oscillating boundary

Denis Borisov; Giuseppe Cardone; Luisa Faella; Carmen Perugia

Abstract In a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small. On the oscillating boundary we impose Dirichlet, Neumann or Robin boundary condition. In all cases we describe the homogenized operator, establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one, and prove the estimates for the rate of convergence. These results are obtained as the order of the amplitude of the oscillations is less, equal or greater than that of the period. It is shown that under the homogenization the type of the boundary condition can change.


Complex Variables and Elliptic Equations | 2015

Optimal control for a second-order linear evolution problem in a domain with oscillating boundary

U. De Maio; Luisa Faella; Carmen Perugia

This paper is concerned with the study of homogenization of an optimal control problem governed by a second-order linear evolution equation with a homogeneous Neumann boundary condition in a domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities, with a fixed height, whose size depends on a small parameter . We identify the limit problem and we remark that both limit state equation and limit cost are different from those ones at level.


Asymptotic Analysis | 2013

Estimates in homogenization of degenerate elliptic equations by spectral method

Giuseppe Cardone; Svetlana E. Pastukhova; Carmen Perugia

We study the homogenization of elliptic equations stated in L 2 -space with degenerate weight. Both coefficients of the differential operator and the weight are e-periodic and highly oscillating as e tends to zero. Under minimal hypotheses on the coefficients and the weight we prove estimates of order e and e 2 for L 2 -norm of the difference between the exact solution and its appropriate approximations by L 2 -norm of the right-side function. The spectral method based on Bloch decomposition is used. In the case of nonunique solution provided that the weight is not regular we consider estimates for any of so-called


Nodea-nonlinear Differential Equations and Applications | 2007

Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boundary

Tiziana Durante; Luisa Faella; Carmen Perugia


Ricerche Di Matematica | 2014

Optimal control problem for an anisotropic parabolic problem in a domain with very rough boundary

U. De Maio; Luisa Faella; Carmen Perugia


Boundary Value Problems | 2015

Optimal control for evolutionary imperfect transmission problems

Luisa Faella; Carmen Perugia


Nonlinear Oscillations | 2004

Homogenization of the Robin problem in a thick multilevel junction

U. De Maio; T. A. Mel’nyk; Carmen Perugia


Boundary Value Problems | 2014

Homogenization of a Ginzburg-Landau problem in a perforated domain with mixed boundary conditions

Luisa Faella; Carmen Perugia


Zeitschrift für Angewandte Mathematik und Physik | 2017

Optimal control of rigidity parameters of thin inclusions in composite materials

A. M. Khludnev; Luisa Faella; Carmen Perugia

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Denis Borisov

University of Hradec Králové

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A. M. Khludnev

Novosibirsk State University

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Sergey A. Nazarov

Saint Petersburg State University

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T. A. Mel’nyk

Taras Shevchenko National University of Kyiv

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U. De Maio

Taras Shevchenko National University of Kyiv

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