Geodesic
A priori properties of solutions of nonlinear equations with degenerate coercivity and $L^1$-data
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, Tome 16 (2006), pp. 47-67.

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A Dirichlet problem for a second-order nonlinear elliptic equation in the general divergent form with a right-hand side from $L^1$ is considered. The high-order coefficients in the equation are supposed to satisfy the degenerate coercivity condition. The main results concern a priori properties of summability and some estimates of entropy solutions of this problem. 
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A. A. Kovalevsky. A priori properties of solutions of nonlinear equations with degenerate coercivity and $L^1$-data. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, Tome 16 (2006), pp. 47-67. http://geodesic.mathdoc.fr/item/CMFD_2006_16_a4/

[1] Gilbarg D., Trudinger N. S., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[2] Kovalevskii A. A., “O summiruemosti reshenii nelineinykh ellipticheskikh uravnenii s pravymi chastyami iz klassov, blizkikh k $L^1$”, Matem. zametki, 70:3 (2001), 375–385 | MR | Zbl

[3] Kovalevskii A. A., “Entropiinye resheniya zadachi Dirikhle dlya odnogo klassa nelineinykh ellipticheskikh uravnenii chetvertogo poryadka s $L^1$-pravymi chastyami”, Izvestiya Rossiiskoi AN. Ser. matem., 65:2 (2001), 27–80 | MR | Zbl

[4] Kovalevskii A. A., “O summiruemosti reshenii nelineinykh ellipticheskikh uravnenii s pravymi chastyami iz logarifmicheskikh klassov”, Matem. zametki, 74:5 (2003), 676–685 | MR | Zbl

[5] Alvino A., Boccardo L., Ferone V., Orsina L., Trombetti G., “Existence results for nonlinear elliptic equations with degenerate coercivity”, Ann. Mat. Pura Appl., IV. Ser., 182 (2003), 53–79 | DOI | MR | Zbl

[6] Alvino A., Ferone V., Trombetti G., “Nonlinear elliptic equations with lower-order terms”, Diff. Int. Equations, 14 (2001), 1169–1180 | MR | Zbl

[7] Bénilan Ph., 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 (1995), 241–273 | MR | Zbl

[8] Betta M. F., Del Vecchio T., Posteraro M. R., “Existence and regularity results for nonlinear degenerate elliptic equations with measure data”, Ric. Mat., 47 (1998), 277–295 | MR | Zbl

[9] Blanchard D., Murat F., Redwane H., “Existence et unicité de la solution renormalisée d'un problème parabolique non linéaire assez général”, C. R. Acad. Sci. Paris. Serie I, 329 (1999), 575–580 | MR | Zbl

[10] Boccardo L., Dall'Aglio A., Orsina L., “Existence and regularity results for some elliptic equations with degenerate coercivity”, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 51–81 | MR | Zbl

[11] Boccardo L., Gallouët T., “Non-linear elliptic and parabolic equations involving measure data”, J. Funct. Anal., 87 (1989), 149–169 | DOI | MR | Zbl

[12] Boccardo L., Gallouët T., “Nonlinear elliptic equations with right hand side measures”, Comm. Partial Differential Equations, 17 (1992), 641–655 | DOI | MR | Zbl

[13] Boccardo L., Gallouët T., “Summability of the solutions of nonlinear elliptic equations with right hand side measures”, J. Convex Analysis, 3 (1996), 361–365 | MR | Zbl

[14] Kovalevsky A. A., On a strict condition of limit summability of solutions of nonlinear elliptic equations with $L^1$-right-hand sides, Preprint Inst. Appl. Math. Mech. of NAS of Ukraine, Donetsk, Ukraine, 2003

[15] Kovalevsky A. A., “The Dirichlet problem for nonlinear equations with degenerate coercivity and $L^1$-data”, Tr. IPMM NAN Ukrainy, 10, 2005, 72–78 | MR | Zbl

[16] Porretta A., “Nonlinear equations with natural growth terms and measure data”, Proceedings of the 2002 Fez Conference on Partial Differential Equations, Electron. J. Differ. Equ. Conf., 9, 2002, 183–202 | MR