177,031 research outputs found
Abstract differential equations of elliptic type with general Robin boundary conditions in Hoelder spaces
No full textIn this article, we prove some new results on abstract second-order differential equations of elliptic type with general Robin boundary conditions. The study is performed in Holder spaces and uses the well-known Da Prato-Grisvard sum theory. We give necessary and sufficient conditions on the data to obtain a unique strict solution satisfying the maximal regularity property. This work completes the ones studied by Favini et al. [A. Favini, R. Labbas, S. Maingot, H. Tanabe, and A. Yagi, Necessary and sufficient conditions in the study of maximal regularity of elliptic differential equations in Holder spaces, Discrete Contin. Dyn. Syst. 22 (2008), pp. 973-987] and Cheggag et al. [M. Cheggag, A. Favini, R. Labbas, S. Maingot and A. Medeghri, Sturm-Liouville problems for an abstract differential equation of elliptic type in UMD spaces, Differ. Int. Eqns 21(9-10) (2008), pp. 981-1000]
Study of boundary value and transmission problems governed by a class of variable operators verifying the Labbas-Terreni non commutativity assumption
No full textInternational audienceThe aim of this work is the study of some transmission problems, which are written as an abstract second order differential equation of elliptic type with variable operator coefficients, in the framework of Hölder spaces. Here, we do not assume the differentiability of the resolvent operators. However, we suppose that the family of variable operators verifies the Labbas-Terreni assumption inspired by the sum theory and similar to the Acquistapace-Terreni one. We use Dunford calculus, interpolation spaces and semigroup theory in order to obtain existence, uniqueness and maximal regularity results for the solution of the problem
NEW results on complete elliptic equations With robin boundary coefficient-operator conditions in non commutative case
No full textIn this paper, we prove some new results on operational second order differential equations of elliptic type with general Robin boundary conditions in a non-commutative framework. The study is performed when the second member belongs to a Sobolev space. Existence, uniqueness and optimal regularity of the classical solution are proved using interpolation theory and results on the class of operators with bounded imaginary powers. We also give an example to which our theory applies. This paper improves naturally the ones studied in the commutative case by M. Cheggag, A. Favini, R. Labbas, S. Maingot and A. Medeghri: in fact, introducing some operational commutator, we generalize the representation formula of the solution given in the commutative case and prove that this representation has the desired regularity
Transmission problems in a thin layer set in the framework of the Hölder spaces: Resolution and impedance concept
No full textAbstractWe consider a family of singular transmission problems depending on some small positive parameter δ set in the juxtaposition of two rectangular domains. They are written in the form of abstract elliptic equations and the study, here, is given in the Hölder spaces completing in this way the work in Lp cases given in [A. Favini, R. Labbas, K. Lemrabet, S. Maingot, Study of the limit of transmission problems in a thin layer by the sum theory of linear operators, Rev. Mat. Complut. 18 (1) (2005) 143–176]. In this first part, we present a new approach for the resolution of these problems by using the concept of impedance operator. This method is different of the one performing a rescaling in the thin layer, see [A. Favini, R. Labbas, K. Lemrabet, S. Maingot, Study of the limit of transmission problems in a thin layer by the sum theory of linear operators, Rev. Mat. Complut. 18 (1) (2005) 143–176]. It leads to obtain direct and simplified problems. We use the Dunford calculus and some techniques similar to that in [R. Labbas, Problèmes aux limites pour une équation différentielle abstraite de type elliptique, Thèse d'état, Université de Nice, 1987; A. Favini, R. Labbas, S. Maingot, H. Tanabe, A. Yagi, Unified study of elliptic problems in Hölder spaces, C. R. Math. Acad. Sci. Paris 134 (2005); G. Dore, A. Favini, R. Labbas, K. Lemrabet, S. Maingot, A transmission problem in a thin layer, Part I, Sharp estimates, in press], to prove existence, uniqueness, results and some specific estimates on the impedance operator. This study will allow us, in a forthcoming work, to obtain respectively optimal regularities and the limit problem when δ→0
Étude dans les espaces de Hölder de problèmes aux limites et de transmission dans un domaine avec couche mince.
No full textWe consider a family (Pδ)δ>0 of boundary value and transmission problems in a domain with thin layer, written in the form of second order abstract differential equation of elliptic type. A new approach for the resolution of (Pδ)δ>0 is presented in this work using the physical concept of impedance. This method is different of the one performing a rescaling in the thin layer, see [Favini A., Labbas R., Lemrabet K. and Maingot S.]. It leads to obtain direct and simplified problems. Where the thin layer effect is completely described by the impedance operator. The techniques employed are primarily based on the functional calculation of Dunford, the semigroups theory, the interpolation and some ideas of work in [R. Labbas, Thesis], [Dore G., Favini A., Labbas R., Lemrabet K. and Maingot S.] and [Favini A., Labbas R., Maingot S., Tanabe H., Yagi A.]. We obtain existence, uniqueness and maximal regularities new results in the Hölder spaces for the fixed and then we study the limit passage when δ→0 of (Pδ)δ>0. This work complete thus what was obtained in the framework Lp, see [Favini A., Labbas R., Lemrabet K. and Maingot S.].On considère une famille (Pδ)δ>0 de problèmes aux limites et de transmission dans un domaine avec couche mince, écrit sous la forme d'une équation différentielle d'ordre deux abstraite de type elliptique . Une nouvelle approche pour la résolution de (Pδ)δ>0 est présentée dans ce travail utilisant le concept physique d'impédance. Cette méthode est différente de celle qui utilise un changement d'échelle sur la couche mince voir [Favini A., Labbas R., Lemrabet K. and Maingot S.]. Elle permet d'obtenir un problème direct et simplifié où l'effet de la couche mince se retrouve complètement décrit par l'opérateur d'impédance. Les techniques employées sont essentiellement basées sur le calcul fonctionnel de Dunford, la théorie des semi-groupes, l'interpolation et quelques idées des travaux de [R. Labbas, Thèse d'état], [Dore G., Favini A., Labbas R., Lemrabet K. and Maingot S.] et [Favini A., Labbas R., Maingot S., Tanabe H., Yagi A.]. On obtient des résultats nouveaux d'existence, d'unicité et de régularité maximale dans les espaces de Hölder pour fixé et ensuite on étudie le passage à la limite quand δ→0 de (Pδ)δ>0. Ce travail complète ainsi ce qui a été obtenu dans le cadre Lp, voir [Favini A., Labbas R., Lemrabet K. and Maingot S.]
Boundary value problem for elliptic differential equations in non-commutative cases
No full textWe consider a boundary value problem for elliptic differential equations in non-commutative case
Resolution and optimal regularity for a biharmonic equation with impedance boundary conditions and some generalizations
No full textA biharmonic equation with an impedance (non standard) boundary condition and more general equations are considered
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Study of a Complete Abstract Differential Equation of Elliptic Type with Variable Operator Coefficients, I
No full textDifferential Equation of Elliptic Type with Variable Operator Coefficients, I Angelo FAVINI, Rabah LABBAS, Keddour LEMRABET, and Boubaker-Khaled SADALLAH Universit` degli Studi di Bologna a Laboratoire de Math´ ematiques Appliqu´ ees Dipartimento di Matematica Universit´ du Havre e Piazza di Porta S. U.F.R Sciences et Techniques, B.P 540 Donato 5, 40126 Bologna -- Italy 76058 Le Havre -- France [email protected] [email protected] Laboratoire EDP et Hist. Maths Lab oraoire AMNEDP Ecole Normale Sup´ erieure Facult´ des Maths, USTHB e 16050 Kouba, Alger -- Algeria BP 32, El Alia, Bab Ezzouar 16111 Alger -- Algeria [email protected] [email protected] Received: May 16, 2007 Accepted: August 30, 2007The aim of this first work is the resolution of an abstract complete second order differential equation of elliptic type with variable operator coefficients set in a small length interval. We obtain existence, uniqueness and maximal regularity results under some appropriate differentiability assumptions combining those of Yagi [13] and Da Prato-Grisvard [6]. An example for the Laplacian in a regular domain of R³ will illustrate the theory. A forthcoming work (Part II) will complete the present one by the study of the Steklov-Poincaré operator related to this equation when the length δ of the interval tends to zero
- …
