论文信息 - On a nonlocal problem with integral boundary conditions for a multidimensional elliptic equation

On a nonlocal problem with integral boundary conditions for a multidimensional elliptic equation

This work is devoted to the investigation of the nonclassical problem for a multidimensional elliptic equation with two integral boundary conditions. By introducing special multipliers we prove the uniqueness of the solution and obtain new a priori estimates, which permit one to establish the existence of a solution in the corresponding Sobolev spaces.

[1] R. Dautray,et al. Analyse mathématique et calcul numérique pour les sciences et les techniques , 1984 .

[2] M. Sapagovas. On the stability of a finite-difference scheme for nonlocal parabolic boundary-value problems , 2008 .

[3] W. McLean. Strongly Elliptic Systems and Boundary Integral Equations , 2000 .

[4] Yuandi Wang. Solutions to nonlinear elliptic equations with a nonlocal boundary condition , 2002 .

[5] R. Lazarov,et al. Finite volume element approximations of nonlocal reactive flows in porous media , 2000 .

[6] J. R. Cannon,et al. The solution of the heat equation subject to the specification of energy , 1963 .

[7] M. Sapagovas. Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions , 2008 .

[8] S. Messaoudi,et al. A NONLOCAL MIXED SEMILINEAR PROBLEM FOR SECOND-ORDER HYPERBOLIC EQUATIONS , 2003 .

[9] Mehdi Dehghan,et al. On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation , 2005 .