This article is cited in 3 papers

General regularizing functionals for solving ill-posed problems in Lebesgue spaces

A. S. Leonov

Moscow Engineering Physics Institute (State University)

Abstract: We study sufficient conditions for general integral functionals in Lebesgue spaces to possess regularizing properties required for solving nonlinear ill-posed problems. We select special classes of such functionals: uniformly convex and quasiuniformly convex (in the extended sense). We give a series of examples and, in particular, a functional that can be used in a generalized version of the maximum entropy method in Lebesgue spaces.

Keywords: regularization, ill-posed problem, Lebesgue space, uniformly (quasiuniformly) convex functional, $H$-property, maximum entropy method.

UDC: 514.13

Received: 19.02.2002

 English version: Siberian Mathematical Journal, 2003, 44:6, 1015–1026q

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