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Estimates for solutions of elliptic equations in a limit case

Published online by Cambridge University Press:  17 April 2009

Ester Giarrusso  and
Guido Trombetti
Ester Giarrusso
Affiliation:
Dipartimento di Matematica ed Applicazioni, “R. Caccioppoli”, Universita di Napoli, via Mezzocannone, 8; 80134 Napoli, Italia
Guido Trombetti
Affiliation:
Dipartimento di Matematica ed Applicazioni, “R. Caccioppoli”, Universita di Napoli, via Mezzocannone, 8; 80134 Napoli, Italia
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Let u be a week solution of homogeneous Dirichlet problem for a second order elliptic equation of divergence form, in a bounded open subset of ℝn. We prove, that if the right hand side of the equation is an element of H−1, n(Ω), then u belongs to the Orlicz space LΦ where Φ(t) = exp(|t|n/(n−1)) − 1. We employ the properties of the Schwartz symmetrization thus obtaining the “best” constant of the estimate.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 3 , December 1987 , pp. 425 - 434
Copyright
Copyright © Australian Mathematical Society 1987

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