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Comparison results for PDEs with a singular potential

Published online by Cambridge University Press:  12 July 2007

Juan Dávila  and
Louis Dupaigne
Juan Dávila
Affiliation:
Department of Mathematics, Hill Centre, 110 Frelinghuysen Road Rutgers, The State University of New Jersey, Piscataway, NJ 08854-8019, USA (davila@math.rutgers.edu)
Louis Dupaigne
Affiliation:
Laboratoire d'analyse numérique, Université Pierre et Marie Curie, Boite courrier 187, 75252 Paris Cedex 05, France (dupaigne@math.rutgers.edu)
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Abstract

Several comparison results are obtained for solutions to linear elliptic and parabolic equations with a singular potential. Solutions to these equations are singular in many cases, and our results roughly say that they all have comparable singularities, provided that they belong to an appropriate space. We formulate the hypothesis on the potential in terms of an inequality, which in the case of the well-known inverse-square potential, is a consequence of an improvement of Hardy's inequality due to Vázquez and Zuazua.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 1 , February 2003 , pp. 61 - 83
Copyright
Copyright © Royal Society of Edinburgh 2003

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