Geodesic
Solvability of nonlocal boundary-value problems for the Laplace equation in the ball
Electronic journal of differential equations, Tome 2014 (2014)
In this article, we consider a class of nonlocal problems for the Laplace equation with boundary operators of fractional order. We prove the existence, uniqueness and a representation of the solutions. Also it is shown that the smoothness of solutions in Holder classes depends on the order of the boundary operators.
Classification : 35J15, 35J25, 34B10, 26A33, 31A05, 31B05
Keywords: Riemann-Liouville operator, Caputo operator, periodic problem, antiperiodic problem, nonlocal problem, Laplace equation, Poisson kernel, harmonic function 
@article{EJDE_2014__2014__a33,
     author = {Sadybekov,  Makhmud A. and Turmetov,  Batirkhan Kh. and Torebek,  Berikbol T.},
     title = {Solvability of nonlocal boundary-value problems for the {Laplace} equation in the ball},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1298.35042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a33/}
}
TY  - JOUR
AU  - Sadybekov,  Makhmud A.
AU  - Turmetov,  Batirkhan Kh.
AU  - Torebek,  Berikbol T.
TI  - Solvability of nonlocal boundary-value problems for the Laplace equation in the ball
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a33/
LA  - en
ID  - EJDE_2014__2014__a33
ER  - 
%0 Journal Article
%A Sadybekov,  Makhmud A.
%A Turmetov,  Batirkhan Kh.
%A Torebek,  Berikbol T.
%T Solvability of nonlocal boundary-value problems for the Laplace equation in the ball
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a33/
%G en
%F EJDE_2014__2014__a33
Sadybekov,  Makhmud A.; Turmetov,  Batirkhan Kh.; Torebek,  Berikbol T. Solvability of nonlocal boundary-value problems for the Laplace equation in the ball. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a33/