Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data

Fiorenza, Alberto; Prignet, Alain

doi:10.1051/cocv:2003015

Fiorenza, Alberto ; Prignet, Alain

ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 317-341

Résumé

We study the sequence $u_{n}$ , which is solution of $- div (a (x, 𝔻 u_{n})) + Φ^{''} (| u_{n} |) u_{n} = f_{n} + g_{n}$ in $Ω$ an open bounded set of $𝐑^{N}$ and $u_{n} = 0$ on $\partial Ω$ , when $f_{n}$ tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the $N$ -function $Φ$ , and prove a non-existence result.

MR Zbl

DOI : 10.1051/cocv:2003015

Classification : 35J60, 46E30, 31C45
Keywords: elliptic equation, Orlicz space, measure, capacity

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     author = {Fiorenza, Alberto and Prignet, Alain},
     title = {Orlicz capacities and applications to some existence questions for elliptic {PDEs} having measure data},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {317--341},
     year = {2003},
     publisher = {EDP Sciences},
     volume = {9},
     doi = {10.1051/cocv:2003015},
     mrnumber = {1966536},
     zbl = {1075.35012},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv:2003015/}
}

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Fiorenza, Alberto; Prignet, Alain. Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 317-341. doi: 10.1051/cocv:2003015

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