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On a nonlocal problem with integral boundary conditions for a multidimensional elliptic equation. (English) Zbl 1205.35085
Summary: This work is devoted to the investigation of a 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.

MSC:
35J60 Nonlinear elliptic equations
35J15 Second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35B45 A priori estimates in context of PDEs
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