Porretta: Absorption effects for some elliptic equations with singularities

Porretta, A.:
Absorption effects for some elliptic equations with singularities
Bollettino dell'Unione Matematica Italiana Serie 8 8-B (2005), fasc. n.2, p. 369-395, Unione Matematica Italiana (English)
pdf (311 Kb), djvu (332 Kb). | MR2149390 | Zbl 1151.35028

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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].

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Referenze Bibliografiche