Abstract
We prove here some existence, uniqueness, and regularity results for a weak solution of a quasilinear elliptic singular problem posed in a two-component domain. The difficulty arises in dealing simultaneously with the quasilinear matrix field, the singular datum, and the interface condition.
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References
Arcoya, D., Boccardo, L., Leonori, T., Porretta, A.: Some elliptic problems with singular natural growth lower order terms. J. Differ. Equ. 249(11), 2771–2795 (2010)
Beltran, R.J.: Homogenization of a quasilinear elliptic problem in a two component domain with an imperfect interface. Master Thesis, University of the Philippines (2014)
Beltran, R.J., Cabarrubias, C., Roque, R.: On the solution of a class of a quasilinear elliptic partial differential equation. Philipp. J. Sci. MS 15-057R (to appear)
Cabarrubias, B., Donato, D.: Existence and uniqueness for a quasilinear elliptic problem with nonlinear Robin conditions. Carpathian J. Math. 27, 173–184 (2011)
Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Clarendon Press, Oxford (1947)
Chourabi, I., Donato, P.: Bounded solutions for a quasilinear singular problem with nonlinear Robin boundary conditions. Differ. Integr. Equ. 26, 975–1008 (2013)
Chipot, M.: Elliptic Equations: An Introductory Course: Birkhäuser Advanced Texts: Basler Lehrbücher. Birkhäuser Verlag, Basel (2009)
Donato, P., Giachetti, D.: Existence and homogenization for a singular problem through rough surfaces. SIAM J. Math. Anal. 48(6), 4047–4087 (2016)
Donato, P., Monsurrò, S., Raimondi, F.: Existence and uniqueness results for a class of singular elliptic problems in perforated domains. Ricerche Mat. (2016). doi:10.1007/s11587-016-0303-y
Giachetti, D., Murat, F.: An elliptic problem with a lower order term having singular behaviour. Boll. Unione Mat. Ital. 2(9), 349–370 (2009)
Giachetti, D., Petitta F., Segura de Leon, S.: Elliptic equations having a singular quadratic gradient term and a sign changing datum. Commun. Pure Appl. Anal. 11, 1875–1895 (2012)
Giachetti, D., Martínez-Aparicio, J., Murat, F.: An elliptic equation with a mild singularity at u = 0: existence and homogenization. J. Math. Pures Appl. (9), http://dx.doi.org/10.1016/j.matpur.2016.04.007 (2016)
Giachetti, D., Martínez-Aparicio, J., Murat, F.: Definition, existence, stability and uniqueness of the solution to a similar elliptic problem with a strong singularity at u = 0. Ann. Sc. Norm. Super. Pisa (2017, to appear)
Monsurrò, S.: Homogenization of a two-component composite with interfacial thermal barrier. Adv. Math. Sci. Appl. 13, 43–63 (2003)
Stampacchia, G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15(1), 189–258 (1965)
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Donato, P., Raimondi, F. (2017). Existence and Uniqueness Results for a Class of Singular Elliptic Problems in Two-Component Domains. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_8
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DOI: https://doi.org/10.1007/978-3-319-59384-5_8
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