Rendiconti Lincei - Matematica e Applicazioni


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Volume 22, Issue 4, 2011, pp. 513–523
DOI: 10.4171/RLM/612

Published online: 2011-12-14

$W^{1,1}_0$ minima of noncoercive functionals

Lucio Boccardo[1], Gisella Croce[2] and Luigi Orsina[3]

(1) Università di Roma La Sapienza, Italy
(2) Université du Havre, Le Havre, France
(3) Università di Roma La Sapienza, Italy

We study an integral non coercive functional defined on $H^1_0(\Omega)$, proving the existence of a minimum in $W^{1,1}_0 (\Omega)$.

Keywords: Integral functionals, direct methods of the calculus of variations, coercivity, lower order terms

Boccardo Lucio, Croce Gisella, Orsina Luigi: $W^{1,1}_0$ minima of noncoercive functionals. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), 513-523. doi: 10.4171/RLM/612