On solvability of a nonlocal problem for the Laplace equation with the fractional-order boundary operator. (English) Zbl 1304.35732
Summary: In the present work, we study properties of some integro-differential operators of the Hadamard-Marchaud type in the class of harmonic functions. As an application of these properties, we consider the question of the solvability of a nonlocal boundary value problem for the Laplace equation in the unit ball.
MSC:
| 35R09 | Integro-partial differential equations |
| 35R11 | Fractional partial differential equations |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 26A33 | Fractional derivatives and integrals |
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