数学与计算机科学 |
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一类具退化强制的椭圆方程在加权Sobolev空间中重整化解的存在性 |
代丽丽 |
通化师范学院 数学学院, 吉林 通化 134002 |
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Existence of renormalized solutions for a degenerate elliptic equation with degenerate coercivity in weighted Sobolev spaces |
DAI Lili |
Institute of Mathematics, Tonghua Normal University, Tonghua 134002, Jilin Province, China |
[1] BOCCARDO L, DALL'AGLIO A, ORSINA L. Existence and regularity results for some elliptic equations with degenerate coercivity[J].Atti del Semimario Matematico e Fisico dell' Universitã di Modena, 1998, 46:51-82.
[2] DAIL L, GAO W J, LI Z Q. Existence of solutions for degenerate elliptic problems in weighted Sobolev space[J]. Journal of Function Spaces, 2015, 2015(71):1-9.
[3] GIACHETTI D, PORZIO M M. Existence results for some nonuniformly elliptic equations with irregular data[J]. Journal of Mathematical Analysis and Applications, 2001, 257(1):100-130.
[4] GIACHETTI D, PORZIO M M. Elliptic equations with degenerate coercivity:Gradient regularity[J].Acta Mathematica Sinica, 2003, 19(2):349-370.
[5] PORRETTA A. Uniqueness and homogenization for a class of non coercive operators in divergence form[J].Atti del Semimario Matematico e Fisico dell' Universitã di Modena, 1998, 46:915-936.
[6] CROCE G. The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity[J]. Rendiconti di Matematica, 2007, 27:299-314.
[7] LEONE C, PORRETTA A. Entropy solutions for nonlinear elliptic equations in L1(Ω)[J]. Nonlinear Analysis Theory Methods and Applications, 1998, 32(3):325-334.
[8] BOCCARDO L, CROCE G, ORSINA L. Nonlinear degenerate elliptic problems with W01,1(Ω) solutions[J]. Manuscripta Mathematica, 2012, 137(3/4):419-439.
[9] GOL'DSHTEIN V, UKHLOV A. Weighted Sobolev spaces and embedding theorems[J].Transactions of the American Mathematical Society, 2009, 361(7):3829-3850.
[10] DRÁBEK P, KUFNER A, MUSTONEN V. Pseudo-monotonicity and degenerated or singular elliptic operators[J]. Bulletin of the Australian Mathematical Society,1998,58(2):213-221.
[11] AZORERO J P G, ALONSO I P. Hardy inequalities and some critical elliptic and parabolic problems[J]. Journal of Differential Equations, 1998, 144(2):441-476.
[12] BLANCHARD D. Truncations and monotonicity methods for parabolic equations[J].Nonlinear Analysis:Theory, Methods and Applications, 1993, 21(10):725-743.
[13] BLANCHARD D,MURAT F, REDWANE H. Existence and uniqueness of a renormalized solution for a fairly general class of nonlinear parabolic problems[J]. Journal of Differential Equations, 2001, 177(2):331-374.
[14] BENILAN P, BREZIS H, CRANDALL M G. A semilinear equation in L1(RN)[J]. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze(Serie IV), 1975, 2(4):523-555.
[15] LIONS J L. Quelques Méthodes de Résolution des Problemes aux Limites Nonlinéaires[M]. Paris:Dunod, 1969.
[16] SCHAFT A V D. Nonlinear systems analysis:M. Vidyasagar[J]. Automatica, 1994, 30(10):1631-1632. |
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