Uniqueness result for a class of singular elliptic problems in two-component domains. (English) Zbl 1433.35115
Summary: In this work we prove a uniqueness result for a quasilinear singular elliptic problem posed in a two-component domain. We prescribe a Dirichlet condition on the exterior boundary, while we prescribe a continuous flux and a jump of the solution proportional to the flux on the interface.
MSC:
| 35J62 | Quasilinear elliptic equations |
| 35J75 | Singular elliptic equations |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
quasilinear elliptic equations; singular equations; two-component domains; jump boundary conditions; uniqueness resultReferences:
| [1] | Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Clarendon Press, Oxford (1947) · Zbl 0029.37801 |
| [2] | Chipot, M.: Elliptic Equations: An Introductory Course. Birkhäuser Advanced Texts, Basler Lehrbücher (2009) · Zbl 1171.35003 · doi:10.1007/978-3-7643-9982-5 |
| [3] | Donato, P.; Giachetti, D., Existence and homogenization for a singular problem through rough surfaces, SIAM J. Math. Anal., 48, 4047-4087 (2016) · Zbl 1357.35154 · doi:10.1137/15M1032107 |
| [4] | Donato, P.; Monsurrò, S.; Raimondi, F., Existence and uniqueness results for a class of singular elliptic problems in perforated domains, Ric. Mat., 66, 333 (2016) · Zbl 1381.35050 · doi:10.1007/s11587-016-0303-y |
| [5] | Donato, P.; Raimondi, F.; Costanda, C. (ed.); Dalla Riva, M. (ed.); Lamberti, PD (ed.); Musolino, P. (ed.), Existence and uniqueness results for a class of singular elliptic problems in two-component domains, No. 1, 83-93 (2017), Basel · Zbl 1404.35189 |
| [6] | Monsurrò, S., Homogenization of a two-component composite with interfacial thermal barrier, Adv. Math. Sci. Appl., 13, 43-63 (2003) · Zbl 1052.35022 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
