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S. C. Pandey - One of the best experts on this subject based on the ideXlab platform.

  • Unified integral formulae pertaining to Elliptic-Type integrals
    Rendiconti del Circolo Matematico di Palermo (1952 -), 2014
    Co-Authors: S. C. Pandey
    Abstract:

    Integrals involving families of Elliptic-Type integrals have their importance in certain problems pertaining to the study of crystallographic minimal surface and in the theory of scattering of acoustic or electromagnetic waves. By the use of some explicit representations of the unified Elliptic-Type integrals, various integrals and multiple integrals, involving a unified family of Elliptic-Type integrals are derived in the present investigation. The results derived in this article are of manifold generality and provide relevant connections with the large number of known results established earlier.

  • A unified Elliptic-Type integral and associated recurrence relations
    Indian Journal of Pure and Applied Mathematics, 2013
    Co-Authors: S. C. Pandey
    Abstract:

    Elliptic-Type integrals have their importance or potential in certain problems in radiation physics and nuclear technology. A number of earlier works on the subject contains several interesting unifications and generalizations of some significant families of Elliptic-Type integrals. Beside explicit representations of certain families of unified Elliptic-Type integrals, contour integral representation, various recurrence relations are derived in the present investigation. The results derived in this article are of manifold generality and provide extensions and unification to the large number of known results established earlier.

  • On certain generalized families of unified Elliptic-Type integrals pertaining to Euler integrals and generating functions
    Rendiconti del Circolo Matematico di Palermo, 2009
    Co-Authors: V. B. L. Chaurasia, S. C. Pandey
    Abstract:

    Elliptic-Type integrals have their importance and potential in certain problems in radiation physics and nuclear technology. A number of earlier works on the subject contains several interesting unifications and generalizations of some significant families of Elliptic-Type integrals. The present paper is intended to obtain certain new theorems on generating functions. The results obtained in this paper are of manifold generality and basic in nature. Beside deriving various known and new Elliptic-Type integrals and their generalizations these theorems can be used to evaluate various Euler-Type integrals involving a number of generating functions.

  • Unified Elliptic-Type integrals and asymptotic formulas
    Demonstratio Mathematica, 2008
    Co-Authors: V. B. L. Chaurasia, S. C. Pandey
    Abstract:

    AbstractThe object of the present paper is to consider a unified and extended form of certain families of Elliptic-Type integrals, which have been discussed in number of earlier works on the subject due to their importance and applications in problems arising in radiation physics and nuclear technology. The results obtained are of general character and include the investigations carried out by several authors. We obtain asymptotic formulas for the unified Elliptic-Type integrals.

Ahmed Medeghri - One of the best experts on this subject based on the ideXlab platform.

  • On general Bitsadze–Samarskii problems of Elliptic Type in $$L^{p}$$ L p cases
    Rendiconti del Circolo Matematico di Palermo Series 2, 2021
    Co-Authors: Brahim Hamdi, Stéphane Maingot, Ahmed Medeghri
    Abstract:

    This paper is devoted to the study of General Bitsadze–Samarskii Problems of Elliptic Type in the framework of UMD Banach spaces. Here, we obtain some results about existence, uniqueness and regularity of the solution. We define two Types of solutions (strict and semi-strict solutions) and we give necessary and sufficient conditions on the data to obtain these results.

  • On general Bitsadze–Samarskii problems of Elliptic Type in $$L^{p}$$ L p cases
    Rendiconti del Circolo Matematico di Palermo Series 2, 2021
    Co-Authors: Brahim Hamdi, Stéphane Maingot, Ahmed Medeghri
    Abstract:

    This paper is devoted to the study of General Bitsadze–Samarskii Problems of Elliptic Type in the framework of UMD Banach spaces. Here, we obtain some results about existence, uniqueness and regularity of the solution. We define two Types of solutions (strict and semi-strict solutions) and we give necessary and sufficient conditions on the data to obtain these results.

  • Nonlocal General Boundary Value Problems of Elliptic Type in L p Cases
    Mediterranean Journal of Mathematics, 2015
    Co-Authors: Houari Hammou, Stéphane Maingot, Rabah Labbas, Ahmed Medeghri
    Abstract:

    This paper is devoted to the study of operational second-order differential equations of Elliptic Type with nonregular coefficient-operator boundary conditions. In the framework of UMD spaces, we give some new results by using semi-groups and interpolation theory. We define two Types of solutions: semi-strict and strict solutions. We then characterizes the existence and uniqueness of such solutions.

  • Abstract differential equations of Elliptic Type with general Robin boundary conditions in Hölder spaces
    Applicable Analysis, 2012
    Co-Authors: Mustapha Cheggag, Stéphane Maingot, Angelo Favini, Rabah Labbas, Ahmed Medeghri
    Abstract:

    In 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].

  • Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions in Hölder Spaces
    Applicable Analysis, 2012
    Co-Authors: Mustapha Cheggag, Stéphane Maingot, Angelo Favini, Rabah Labbas, Ahmed Medeghri
    Abstract:

    In this paper we prove some new results on abstract second order differential equations of Elliptic Type with general Robin boundary conditions. The study is performed in Hölder spaces and uses the celebrated 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.

Angelo Favini - One of the best experts on this subject based on the ideXlab platform.

  • Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions in Hölder Spaces
    Applicable Analysis, 2012
    Co-Authors: Mustapha Cheggag, Stéphane Maingot, Angelo Favini, Rabah Labbas, Ahmed Medeghri
    Abstract:

    In this paper we prove some new results on abstract second order differential equations of Elliptic Type with general Robin boundary conditions. The study is performed in Hölder spaces and uses the celebrated 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.

  • Abstract differential equations of Elliptic Type with general Robin boundary conditions in Hölder spaces
    Applicable Analysis, 2012
    Co-Authors: Mustapha Cheggag, Stéphane Maingot, Angelo Favini, Rabah Labbas, Ahmed Medeghri
    Abstract:

    In 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 a Complete Abstract Differential Equation of Elliptic Type with Variable Operator Coefficients, I
    Rev. Mat. Complut., 2008
    Co-Authors: Angelo Favini, Rabah Labbas, Keddour Lemrabet, Boubaker-khaled Sadallah
    Abstract:

    The aim of this fi rst work is the resolution of an abstract complete second order diff erential equation of Elliptic Type with variable operator coeffi cients set in a small length interval. We obtain existence, uniqueness and maximal regularity results under some appropriate di fferentiability 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 delta of the interval tends to zero.

  • On the Solvability of Complete Abstract Differential Equations of Elliptic Type
    Funkcialaj Ekvacioj, 2004
    Co-Authors: Angelo Favini, Rabah Labbas, Hiroki Tanabe, Atsushi Yagi
    Abstract:

    In this work we give some new results on complete abstract second order differential equations of Elliptic Type in a Banach space. The existence and the uniqueness of the strict solution are proved under some natural assumptions generalising previous theorems on the subject.

Stéphane Maingot - One of the best experts on this subject based on the ideXlab platform.

Rabah Labbas - One of the best experts on this subject based on the ideXlab platform.

  • Nonlocal General Boundary Value Problems of Elliptic Type in L p Cases
    Mediterranean Journal of Mathematics, 2015
    Co-Authors: Houari Hammou, Stéphane Maingot, Rabah Labbas, Ahmed Medeghri
    Abstract:

    This paper is devoted to the study of operational second-order differential equations of Elliptic Type with nonregular coefficient-operator boundary conditions. In the framework of UMD spaces, we give some new results by using semi-groups and interpolation theory. We define two Types of solutions: semi-strict and strict solutions. We then characterizes the existence and uniqueness of such solutions.

  • Abstract differential equations of Elliptic Type with general Robin boundary conditions in Hölder spaces
    Applicable Analysis, 2012
    Co-Authors: Mustapha Cheggag, Stéphane Maingot, Angelo Favini, Rabah Labbas, Ahmed Medeghri
    Abstract:

    In 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].

  • Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions in Hölder Spaces
    Applicable Analysis, 2012
    Co-Authors: Mustapha Cheggag, Stéphane Maingot, Angelo Favini, Rabah Labbas, Ahmed Medeghri
    Abstract:

    In this paper we prove some new results on abstract second order differential equations of Elliptic Type with general Robin boundary conditions. The study is performed in Hölder spaces and uses the celebrated 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.

  • Study of a Complete Abstract Differential Equation of Elliptic Type with Variable Operator Coefficients, I
    Rev. Mat. Complut., 2008
    Co-Authors: Angelo Favini, Rabah Labbas, Keddour Lemrabet, Boubaker-khaled Sadallah
    Abstract:

    The aim of this fi rst work is the resolution of an abstract complete second order diff erential equation of Elliptic Type with variable operator coeffi cients set in a small length interval. We obtain existence, uniqueness and maximal regularity results under some appropriate di fferentiability 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 delta of the interval tends to zero.

  • On the Solvability of Complete Abstract Differential Equations of Elliptic Type
    Funkcialaj Ekvacioj, 2004
    Co-Authors: Angelo Favini, Rabah Labbas, Hiroki Tanabe, Atsushi Yagi
    Abstract:

    In this work we give some new results on complete abstract second order differential equations of Elliptic Type in a Banach space. The existence and the uniqueness of the strict solution are proved under some natural assumptions generalising previous theorems on the subject.