Absorption effects for some elliptic equations with singularities

Porretta, A.

Porretta, A.

Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005), p. 369-395 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

We give an expository review of recent results obtained for elliptic equations having natural growth terms of absorption type and singular data. As a new result, we provide an application to the case of lower order terms of subcritical growth, proving a general solvability result with measure data for a class of equations modeled on (1.6).

In questa nota si presenta una breve rassegna di alcuni recenti risultati ottenuti su una classe di equazioni ellittiche con termini di assorbimento a crescita naturale e dati singolari. Si mettono in luce tipici fenomeni (stabilità, esistenza o nonesistenza, singolarità rimovibili, effetti di barriera) dovuti essenzialmente all'effetto regolarizzante dei termini di assorbimento che in alcuni casi può impedire la presenza o la diffusione di singolarità nellequazione. Oltre all'esposizione di risultati già noti, si presenta una nuova applicazione al caso di crescita sottocritica per l'equazione modello (1.6), per la quale dimostriamo un risultato generale di esistenza con dato misura, nelle ipotesi ottimali che estendono la classica condizione di P. Benilan e H. Brezis [4].

Publié le : 2005-06-01

MR 2149390 | Zbl 1151.35028

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     author = {A. Porretta},
     title = {Absorption effects for some elliptic equations with singularities},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {8-A},
     year = {2005},
     pages = {369-395},
     zbl = {1151.35028},
     mrnumber = {2149390},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_2_369_0}
}

Porretta, A. Absorption effects for some elliptic equations with singularities. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 369-395. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_2_369_0/

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