A Variational Inequality for a Degenerate Elliptic Operator Under Minimal Assumptions on the Coefficients

Vitanza, Carmela; Zamboni, Pietro

Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 341-356 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

In this note we obtain the existence and the uniqueness of the solution of a variational inequality associated to the degenerate operator ${}Lu=-\sum^{n}_{i,j=1}(a_{ij}(x)u_{x_{i}}+d_{j}u)_{x_{j}}+\sum^{n}_{i=1}b_{i}u% _{x_{i}}+cu$ assuming the coefficients of the lower terms and the known term belonging to a suitable degenerate Stummel-Kato class. The weight $w$ , which gives the degeneration, belongs to the Muckenoupt class $A^{2}$ .

In questa nota si studia un problema di esistenza e unicità di soluzioni di una disuguaglianza variazionale associata al seguente operatore degenere ${}Lu=-\sum^{n}_{i,j=1}(a_{ij}(x)u_{x_{i}}+d_{j}u)_{x_{j}}+\sum^{n}_{i=1}b_{i}u% _{x_{i}}+cu$ . I coefficienti dei termini di ordine inferiore e del termine noto di (*) appartengono ad una generalizzazione degenere del classico spazio di Stummel-Kato. Il peso $w$ , che fornisce la degenerazione, appartiene alla classe $A_{2}$ di Muckenoupt.

Publié le : 2007-06-01

MR 2339445 | Zbl 1178.49012

@article{BUMI_2007_8_10B_2_341_0,
     author = {Carmela Vitanza and Pietro Zamboni},
     title = {A Variational Inequality for a Degenerate Elliptic Operator Under Minimal Assumptions on the Coefficients},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {341-356},
     zbl = {1178.49012},
     mrnumber = {2339445},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_2_341_0}
}

Vitanza, Carmela; Zamboni, Pietro. A Variational Inequality for a Degenerate Elliptic Operator Under Minimal Assumptions on the Coefficients. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 341-356. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_2_341_0/

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