Abstract
We consider the Dirichlet problem for a class of strongly nonlinear elliptic equations with degenerate coercivity and data in divergence form. We show that some lower order terms have regularizing effects on solutions.
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Alvino A., Boccardo L., Ferone V., Orsina L., Trombetti G.: Existence results for nonlinear elliptic equations with degenerate coercivity. Ann. Mat. Pura Appl. 182, 53–79 (2003)
Alvino A., Ferone V., Trombetti G.: Nonlinear elliptic equations with lower-order terms. Differ. Integr. Equ. 14, 1169–1180 (2001)
Alvino A., Ferone V., Trombetti G.: A priori estimates for a class of nonuniformly elliptic equations. Atti Semin. Mat. Fis. Univ. Modena. 46(suppl.), 381–391 (1998)
Bénilan P., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vazquez J.L.: An L 1-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. IV. Ser. 22, 240–273 (1995)
Benkirane A., Youssfi A.: Regularity for solutions of nonlinear elliptic equations with degenerate coercivity. Ricerche Mat. 56(2), 241–275 (2007)
Benkirane A., Youssfi A., Meskine D.: Bounded solutions for nonlinear elliptic equations with degenerate coercivity and data in an LlogL. Bull. Belg. Math. Soc. Simon Stevin. 15(2), 369–375 (2008)
Benkirane A., Youssfi A.: Existence of bounded solutions for a class of strongly nonlinear elliptic equations in Orlicz-Sobolev spaces. Aust. J. Math. Anal. Appl. 5(1), 1–26 (2008) Art. 7
Boccardo L., Brézis H.: Some remarks on a class of elliptic equations with degenerate coercivity. Boll. Unione Mat. Ital. 6, 521–530 (2003)
Boccardo L., Dall’aglio A., Orsina L.: Existence and regularity results for some nonlinear equations with degenerate coercivity. Atti Sem. Mat. Fis. Univ. Modena 46(suppl.), 51–81 (1998)
Boccardo, L., Gallouët, T., Murat, F.: A unified presentation of two existence results for problems with natural growth. In: Progress in PDE, the Metz surveys 2, 127–137 (1992) [M. Chipot editor, Pitman Res. Notes in Math. Ser., vol. 296. Longman Sci. Tech., Harlow (1993)]
Boccardo L., Segurade Leon S., Trombetti C.: Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term. J. Math. Pures Appl. (9) 80, 919–940 (2001)
Brézis H., Browder F.E.: Some properties of higher order Sobolev spaces. J. Math. Pures Appl. 61, 245–259 (1982)
Cirmi G.R.: Regularity of the solutions to nonlinear elliptic equations with a lower-order term. Nonlinear Anal. 25, 569–580 (1995)
Croce G.: The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity. Rend. Mat. Appl. Serie VII 27, 299–314 (2007)
Della Pietra F.: Existence results for non-uniformly elliptic equations with general growth in the gradient. Differ. Integr. Equ. 21, 821–836 (2008)
Della Pietra, F.: Existence results for some classes of nonlinear elliptic problems. Dottorato thesis, Universit degli Studi di Napoli Federico II (2008)
Kufner, A., John, O., Opic, B.: Function spaces. Academia, Praha (1977)
Leray J., Lions J.L.: Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder. Bull. Soc. Mat. France. 93, 97–107 (1965)
Stampacchia G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Ist. Fourier (Grenoble) 15, 189–258 (1965)
Trombetti C.: Nonuniformly elliptic equations with natural growth in the gradient. Potent. Anal. 18, 391–404 (2003)
Webb J.R.L.: Boundary value problems for strongly nonlinear elliptic equations. J. Lond. Math. Soc. 21, 123–132 (1980)
Youssfi A.: Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces, Electron. J. Diff. Eqns. 2007(54), 1–13 (2007)
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Benkirane, A., Youssfi, A. Regularizing effects of some lower order terms in non-uniformly nonlinear elliptic equations. Ricerche mat. 58, 185–205 (2009). https://doi.org/10.1007/s11587-009-0057-x
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DOI: https://doi.org/10.1007/s11587-009-0057-x