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Some functional inequalities, with application to Green's function

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Abstract

Some elementary inequalities for functional with functional derivatives of given sign are presented and proved. These are then applied to the study of Green's functions for diffusion processes in a medium with sources and sinks (or alternately to Green's functions for the Schrödinger operator). The resulting inequalities are shown to include as quite special cases the super and sub-additive inequalities of potential theory. One consequence of the generalization is that scattering length is also shown to have sub-additive properties.

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Authors and Affiliations

  1. Department of Physics, Columbia University, New York

    J. M. Luttinger & R. Friedberg

  2. Department of Physics, Columbia University and Barnard College, New York

    J. M. Luttinger & R. Friedberg

Authors
  1. J. M. Luttinger
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  2. R. Friedberg
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Additional information

Communicated by M. Kac

This research was supported in part by the National Science Foundation and the U.S. Atomic Energy Commission.

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Luttinger, J.M., Friedberg, R. Some functional inequalities, with application to Green's function. Arch. Rational Mech. Anal. 61, 187–195 (1976). https://doi.org/10.1007/BF00249705

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  • DOI: https://doi.org/10.1007/BF00249705

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