Accès libre

Existence and Regularity for Solution to a Degenerate Problem with Singular Gradient Lower Order Term

   | 11 oct. 2022
À propos de cet article

Citez

[1] Alvino A, Boccardo L, Ferone V, Orsina L, Trombetti G, Existence results for nonlinear elliptic equations with degenerate coercivity, Annali di Matematica, 182 (2003), 53-79.10.1007/s10231-002-0056-y Search in Google Scholar

[2] Arcoya D, Boccardo L, Leonori T, Porretta A, Some elliptic problems with singular natural growth lower order terms, Calc. Var. Partial Differ. Equ, 37 (2010), 363-380.10.1007/s00526-009-0266-x Search in Google Scholar

[3] Arcoya D, Carmona J, Leonori T, Mart‘ınez-Aparicio P.J, Orsina L, Petitta F, Existence and nonexistence of solutions for singular quadratic quasilinear equations, J. Differential Equations, 246 (2009), 4006-4042.10.1016/j.jde.2009.01.016 Search in Google Scholar

[4] Ayadi H, Souilah R, Existence and regularity results for unilateral problems with degenerate coercivity, J. Math. Slovaca, 6 (2019), 1351-1366.10.1515/ms-2017-0313 Search in Google Scholar

[5] Boccardo L, Dirichlet problems with singular and gradient quadratic lower order terms, ESAIM Control Optim. Calculus Var, 14 (2008), 411-426.10.1051/cocv:2008031 Search in Google Scholar

[6] Boccardo L, Dall’Aglio A, Orsina L, Existence and regularity results for some elliptic equations with degenerate coercivity, Dedicated to Prof. C. Vinti (Italian) (Perugia, 1996), Atti Sem. Mat. Fis. Univ. Modena 46 suppl, 5 (1998), 1-81. Search in Google Scholar

[7] Boccardo L, Gallouet T, Strongly nonlinear elliptic equations having natural growth terms and L1 data, Nonlmear Analysis, Theory, Methods Applications, 6 (1992), 573-579. Search in Google Scholar

[8] Boccardo L, Gallouët T, W01,1 solutions in some borderline cases of Calderon-Zygmund theory, J. Differential Equations, 253 (2012), 2698-2714.10.1016/j.jde.2012.07.003 Search in Google Scholar

[9] Boccardo L, Murat F, Puel J.P, Existence de solutions non bornées pour certaines équations quasi-linéaires, Portugaliae Mathematica, 41 (1982), 1-4. Search in Google Scholar

[10] Boccardo L, Murat F, Puel J.P., L estimate for some nonlinear elliptic partial differential equations and application to an existence result, SIAM J. Math. Anal, 23 (1992), 326-333.10.1137/0523016 Search in Google Scholar

[11] Boccardo L, Mérida A.M, Orsina L, A class of quasilinear Dirichlet problems with unbounded coefficients and singular quadratic lower order terms, Milan J. Math, 83 (2015), 157-176.10.1007/s00032-015-0232-3 Search in Google Scholar

[12] Boccardo L, Orsina L, Porzio M.M, Existence results for quasilinear elliptic and parabolic problems with quadratic gradient terms and sources, Adv. Calculus Var, 4 (2011), 397-419. Search in Google Scholar

[13] Croce G, An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term, American Institute of Mathematical Sciences, (2012), 507-730.10.3934/dcdss.2012.5.507 Search in Google Scholar

[14] Crandall M.G, Rabinowitz P.H, Tartar L, On a Dirichlet problem with asingular nonlinearity, Commun. Partial Differ. Equ, 2 (1977), 193-222.10.1080/03605307708820029 Search in Google Scholar

[15] Giachetti D, Murat F, An elliptic problem with a lower order term having singular behaviour Boll, Unione Mat. Ital, 2 (2009), 1-19. Search in Google Scholar

[16] Giachetti D, Petitta F, De León S.S, A priori estimates for elliptic problems with a strongly singular gradient term and a general datum, Differ. Integral Equ, 26 (2010), 302-336. Search in Google Scholar

[17] Giachetti D, Petitta F, De León S.S, Elliptic equations having a singular quadratic gradient term and a changing sign datum, Commun. Pure Appl. Anal, 11 (2012), 1875-1895.10.3934/cpaa.2012.11.1875 Search in Google Scholar

[18] Hirano N, Saccon C, Shioji N, Multiple existence of positive solutions for singular elliptic problems with concave ad convex nonlinearities, Adv. Differ. Equ, 9 (2004), 197-220. Search in Google Scholar

[19] Leoni F, Nonlinear elliptic equatIions in ℝN with absorbing zero order terms, Advances in Differential Equations, 5 (2000), 681-722.10.57262/ade/1356651344 Search in Google Scholar

[20] Lazer A.C, Mckenna P.J, On a singular nonlinear elliptic boundary-value problem, Proc. Am. Math. Soc, 111 (1991), 721-730.10.1090/S0002-9939-1991-1037213-9 Search in Google Scholar

[21] Leoni F, Pellacci B, Local estimates and global existence for strongly nonlinear parabolic equations with locally integrable data, Journal of Evolution Equations, 6 (2006), 113-144.10.1007/s00028-005-0234-7 Search in Google Scholar

[22] Martinez-Aparicio P.J, Singular Dirichlet problems with quadratic gradient, Boll. Unione Mat. Ital, 2 (2009), 559-574. Search in Google Scholar

[23] Lions J.L, Quelques méthodes de résolution des probl‘emes aux limites non linéaires, Dunod, (1969). Search in Google Scholar

[24] Porretta A, Uniqueness and homogeneization for a class of noncoercive operators in divergence form, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 915-936. Search in Google Scholar