Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in L 1 (Ω)
ESAIM: Control, Optimisation and Calculus of Variations, Volume 8  (2002), p. 239-272

In this paper we prove uniqueness results for the renormalized solution, if it exists, of a class of non coercive nonlinear problems whose prototype is -div(a(x)(1+|u| 2 ) p-2 2 u)+b(x)(1+|u| 2 ) λ 2 =finΩ,u=0onΩ, where Ω is a bounded open subset of N , N2, 2-1/N<p<N, a belongs to L (Ω), a(x)α 0 >0, f is a function in L 1 (Ω), b is a function in L r (Ω) and 0λ<λ * (N,p,r), for some r and λ * (N,p,r).

DOI : https://doi.org/10.1051/cocv:2002051
Classification:  35J25,  35J60
Keywords: uniqueness, nonlinear elliptic equations, noncoercive problems, data in L 1
@article{COCV_2002__8__239_0,
     author = {Betta, M. F. and Mercaldo, A. and Murat, Fran\c cois and Porzio, M. M.},
     title = {Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^1(\Omega )$},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     pages = {239-272},
     doi = {10.1051/cocv:2002051},
     zbl = {1092.35032},
     mrnumber = {1932952},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__8__239_0}
}
Betta, M. F.; Mercaldo, A.; Murat, F.; Porzio, M. M. Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^1(\Omega )$. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002) , pp. 239-272. doi : 10.1051/cocv:2002051. http://www.numdam.org/item/COCV_2002__8__239_0/

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