Journal of Elliptic and Parabolic Equations

, Volume 5, Issue 2, pp 349–358 | Cite as

Uniqueness result for a class of singular elliptic problems in two-component domains

  • Patrizia Donato
  • Federica RaimondiEmail author


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.


Uniqueness Quasilinear elliptic equations Singular equations Two-component domains Jump boundary conditions 

Mathematics Subject Classification

35J62 35J75 35A02 



The results of this paper were presented in the International Conference on Elliptic and Parabolic Problems, held in Gaeta, 20–25 may 2019. The authors thank the referee for the useful comments and helpful suggestions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Clarendon Press, Oxford (1947)zbMATHGoogle Scholar
  2. 2.
    Chipot, M.: Elliptic Equations: An Introductory Course. Birkhäuser Advanced Texts, Basler Lehrbücher (2009)CrossRefGoogle Scholar
  3. 3.
    Donato, P., Giachetti, D.: Existence and homogenization for a singular problem through rough surfaces. SIAM J. Math. Anal. 48, 4047–4087 (2016)MathSciNetCrossRefGoogle Scholar
  4. 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). MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Donato, P., Raimondi, F.: Existence and uniqueness results for a class of singular elliptic problems in two-component domains. In: Costanda, C., Dalla Riva, M., Lamberti, P.D., Musolino, P. (eds.) Integral Methods in Science and Engineering, vol. 1, pp. 83–93. Birkhäuser, Basel (2017)zbMATHGoogle Scholar
  6. 6.
    Monsurrò, S.: Homogenization of a two-component composite with interfacial thermal barrier. Adv. Math. Sci. Appl. 13, 43–63 (2003)MathSciNetzbMATHGoogle Scholar

Copyright information

© Orthogonal Publisher and Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Raphaël Salem, CNRS, UMR 6085Université de Rouen NormandieSaint-Étienne du RouvrayFrance

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