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Deficient Coerciveness Estimate for an Abstract Differential Equation with a Parameter Dependent Boundary Conditions

Aissa Aibeche; Angelo Favini; Chahrazed Mezoued

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 535-547
  • ISSN: 0392-4041

Abstract

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In this paper we consider an abstract elliptic differential problem where the equation and the boundary conditions may contain a spectral parameter. We first prove that this problem generates an isomorphism between appropriate spaces and we establish a more precise estimate called coerciveness estimate with defect. The results obtained are applied to study some classes of elliptic, and also possibly degenerate, problems.

How to cite

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Aibeche, Aissa, Favini, Angelo, and Mezoued, Chahrazed. "Deficient Coerciveness Estimate for an Abstract Differential Equation with a Parameter Dependent Boundary Conditions." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 535-547. <http://eudml.org/doc/290424>.

@article{Aibeche2007,
abstract = {In this paper we consider an abstract elliptic differential problem where the equation and the boundary conditions may contain a spectral parameter. We first prove that this problem generates an isomorphism between appropriate spaces and we establish a more precise estimate called coerciveness estimate with defect. The results obtained are applied to study some classes of elliptic, and also possibly degenerate, problems.},
author = {Aibeche, Aissa, Favini, Angelo, Mezoued, Chahrazed},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {535-547},
publisher = {Unione Matematica Italiana},
title = {Deficient Coerciveness Estimate for an Abstract Differential Equation with a Parameter Dependent Boundary Conditions},
url = {http://eudml.org/doc/290424},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Aibeche, Aissa
AU - Favini, Angelo
AU - Mezoued, Chahrazed
TI - Deficient Coerciveness Estimate for an Abstract Differential Equation with a Parameter Dependent Boundary Conditions
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 535
EP - 547
AB - In this paper we consider an abstract elliptic differential problem where the equation and the boundary conditions may contain a spectral parameter. We first prove that this problem generates an isomorphism between appropriate spaces and we establish a more precise estimate called coerciveness estimate with defect. The results obtained are applied to study some classes of elliptic, and also possibly degenerate, problems.
LA - eng
UR - http://eudml.org/doc/290424
ER -

References

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  2. AGRANOVICH, M. S. - VISIK, M. L., Elliptic Problems with a Parameter and Parabolic Problems of General Type, Russian Math. Surveys, 19 (1964), 53-161. MR192188
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  12. LIONS, J. L. - MAGENES, E., Problèmes aux Limites non Homogènes et applications, Vol. I, Dunod, Paris (1968). MR247243
  13. LIONS, J. L. - PEETRE, J., Sur une classe d'espaces d'interpolation, Inst. Hautes Etudes Sci. Publ. Math., 19 (1964), 5-68. Zbl0148.11403MR165343
  14. TRIEBEL, H., Interpolation Theory, Functions Spaces, Differential Operators, North Holland, Amsterdam (1978). Zbl0387.46033MR503903
  15. YAKUBOV, S. Y., Completeness of Root Functions of Regular Differential Operators, Longman, Scientific and Technical, New York (1994). MR1401350
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