A nonlocal boundary-value problem for partial differential equations with constant coefficients belonging to smooth curves
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We have investigated a nonlocal boundary-value problem in a cylindrical domain for partial differential equations with constant coefficients belonging to smooth curves. The solvability of this problem is connected with the problem of small denominators on smooth manifolds, which appear in constructing the solution. We have obtained the conditions of uniqueness and existence of solution of this problem. Finally, we have established the lower metric estimates of small denominators on smooth curves.
KeywordsManifold Partial Differential Equation Lebesgue Measure Smooth Curve Constant Coefficient
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