Geodesic
Solvability of nonlocal boundary-value problems for the Laplace equation in the ball
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a33/}
}
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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/