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Direct and inverse boundary value problems are solved and the solution of an optimization problem is obtained analytically in the case of some nonlinear integral functionals. The plane potential flow of an inviscid fluid is considered in the absence of mass forces (Hyp). The flow – unlimited jet – encounters a symmetrical curvilinear obstacle (the Helmholtz scheme). For inverse problems there are derived singular integral equations and the movement is obtained in the auxiliary canonical half plane. Next, an optimization problem is solved analytically. The design of the optimal airfoil is performed. The drag coefficient and other geometrical parameters are computed in the case of a given distribution of the velocity on the profile. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)