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On minimization of one integral functional by the Ritz method

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Abstract

Using the variational method, we investigate a nonlinear problem with a Bernoulli condition in the form of an inequality on a free boundary. We prove a solvability theorem and establish the convergence of an approximate solution obtained by the Ritz method to the exact solution in certain metrics.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1385–1394, October, 2006.

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Minenko, A.S. On minimization of one integral functional by the Ritz method. Ukr Math J 58, 1570–1581 (2006). https://doi.org/10.1007/s11253-006-0154-x

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  • DOI: https://doi.org/10.1007/s11253-006-0154-x

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