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Nonlinear potentials in function spaces

Published online by Cambridge University Press:  22 January 2016

Murali Rao  and
Zoran Vondraćek
Murali Rao
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Fl 32611-8105, U.S.A., rao@math.ufl.edu
Zoran Vondraćek
Affiliation:
Department of Mathematics, University of Zagreb, BijeniĆka c. 30, 10000 Zagreb, Croatia, vondra@math.hr
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Abstract

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We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capacities, equilibrium potentials and measures of finite energy.

Keywords

31C1531C4546B1046Exx46E3547H07
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 165 , March 2002 , pp. 91 - 116
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

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