We study the stability, with respect to the G-convergence, of the distributional solutions of a degenerate elliptic equation.
Get full access to this article
View all access options for this article.
References
1.
A.Alvino, L.Boccardo, V.Ferone, L.Orsina and G.Trombetti, Existence results for nonlinear elliptic equations with degenerate coercivity, Ann. Mat. Pura Appl.182 (2003), 53–79.
2.
L.Boccardo, Some elliptic problems with degenerate coercivity, Adv. Nonlinear Stud.6 (2006), 1–12.
3.
L.Boccardo and H.Brezis, Some remarks on a class of elliptic equations, Boll. Unione Mat. Ital.6 (2003), 521–530.
4.
L.Boccardo, G.Croce and L.Orsina, A semilinear problem with a solution, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.23(2) (2012), 97–103.
5.
L.Boccardo, G.Croce and L.Orsina, Nonlinear degenerate elliptic problems with solutions, Manuscripta Math.137 (2012), 419–439.
6.
L.Boccardo, A.Dall’Aglio and L.Orsina, Existence and regularity results for some elliptic equations with degenerate coercivity, dedicated to Prof. C. Vinti (Perugia, 1996), Atti Sem. Mat. Fis. Univ. Modena46 (1998), 51–81.
7.
L.Boccardo and P.Marcellini, Sulla convergenza delle soluzioni di disequazioni variazionali, Ann. Mat. Pura Appl.110 (1976), 137–159.
8.
G.Croce, The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity, Rendiconti di Matematica27 (2007), 299–314.
9.
N.G.Meyers, An estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa17 (1963), 189–206.
10.
F.Murat, G-Convergence, Séminaire d’analyse fonctionnelle et numérique, Université d’Alger, 1977–1978, p. 34, multicopied; English translation: F. Murat and L. Tartar, H-convergence, in: Topics in the Mathematical Modelling of Composite Materials, L. Cherkaev and R.V. Kohn, eds, Progress in Nonlinear Differential Equations and Their Applications, Vol. 31, Birkhäuser, Boston, 1998, pp. 21–43.
11.
F.Murat, Compacité par compensation, Ann. Scuola. Norm. Sup. Pisa, Serie IV5 (1978), 489–507.
12.
A.Porretta, Uniqueness and homogenization for a class of noncoercive operators in divergence form, dedicated to Prof. C. Vinti (Perugia, 1996), Atti Sem. Mat. Fis. Univ. Modena46 (1998), 915–936.
13.
S.Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scuola Norm. Sup. Pisa Cl. Sci.22 (1968), 571–597.
14.
L.Tartar, Compensated compactness and applications to partial differential equations, in: Nonlinear Analysis and Mechanics: Heriot Watt Symposium IV, Pitman, San Francisco, 1979, pp. 136–212.