Autovalori di alcune disequazioni variazionali con vincoli puntati sulle derivate
Saccon, Claudio
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993), p. 185-195 / Harvested from Biblioteca Digitale Italiana di Matematica
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Si studiano problemi di autovalori per disequazioni variazionali semilineari ellittiche con un ostacolo puntuale sulla derivata prima della funzione incognita. Si mette in particolare in evidenza il ruolo della «ipotesi di non tangenza» tra il convesso, che viene definito dalla condizione di ostacolo, e la sfera dello spazio funzionale, su cui è naturale studiare un problema di autovalori. Tale condizione viene analizzata in alcuni casi concreti e si indicano alcune ipotesi che, garantendone la validità, danno luogo ad alcuni risultati di esistenza e molteplicità.

Some eigenvalue problems for elliptic semilinear variational inequalities are studied, the main feature being the presence of an obstacle on the first derivative of the unknown function. The role of a «nontangency» assumption is put into evidence: to have existence and multiplicity results one has to check that the convex set, produced by the obstacle condition, and the sphere in the function space, on which it seems natural to study eigenvalue problems, are not tangent. This condition is studied in some problems of the fourth and of the second order and some sufficient conditions for it are found, which allow to get results of existence and multiplicity.

Publié le : 1993-09-01
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     author = {Claudio Saccon},
     title = {Autovalori di alcune disequazioni variazionali con vincoli puntati sulle derivate},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {4},
     year = {1993},
     pages = {185-195},
     zbl = {0801.49013},
     mrnumber = {1250497},
     language = {it},
     url = {http://dml.mathdoc.fr/item/RLIN_1993_9_4_3_185_0}
}

Saccon, Claudio. Autovalori di alcune disequazioni variazionali con vincoli puntati sulle derivate. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993) pp. 185-195. http://gdmltest.u-ga.fr/item/RLIN_1993_9_4_3_185_0/

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