Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods

Alvino, Angelo; Mercaldo, Anna

Bollettino dell'Unione Matematica Italiana, Tome 1 (2008), p. 645-661 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

We consider the homogeneous Dirichlet problem for nonlinear elliptic equations as $-\operatorname{div}a(x,\nabla u)=b(x,\nabla u)+\mu$ where $\mu$ is a measure with bounded total variation. We fix structural conditions on functions $a$ , $b$ which ensure existence of solutions. Moreover, if $\mu$ is an $L^{1}$ function, we prove a uniqueness result under more restrictive hypotheses on the operator.

Publié le : 2008-10-01

MR 2455337 | Zbl 1191.35125

@article{BUMI_2008_9_1_3_645_0,
     author = {Angelo Alvino and Anna Mercaldo},
     title = {Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {1},
     year = {2008},
     pages = {645-661},
     zbl = {1191.35125},
     mrnumber = {2455337},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_3_645_0}
}

Alvino, Angelo; Mercaldo, Anna. Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 645-661. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_3_645_0/

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