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Solvability of nonlocal elliptic problems in dihedral angles. (English. Russian original) Zbl 1130.35344
Math. Notes 72, No. 2, 158-176 (2002); translation from Mat. Zametki 72, No. 2, 178-197 (2002).
Here the author proposes new approach to studying nonlocal problems based on the Green’s formula and conjugate nonlocal problems. Such an approach allows him to remove additional constraints on the corresponding “local” model problem and to obtain necessary and sufficient conditions for the Fredholm solvability of nonlocal problems in plane angles and for the unique solvability of such problems in dihedral angles.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35A08 Fundamental solutions to PDEs
35B45 A priori estimates in context of PDEs
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