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Nonlinear Elliptic Inclusions with Unilateral Constraint and Dependence on the Gradient

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Abstract

We consider a nonlinear Neumann elliptic inclusion with a source (reaction term) consisting of a convex subdifferential plus a multivalued term depending on the gradient. The convex subdifferential incorporates in our framework problems with unilateral constraints (variational inequalities). Using topological methods and the Moreau-Yosida approximations of the subdifferential term, we establish the existence of a smooth solution.

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Acknowledgements

V. Rădulescu was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, Project Number PN-II-PT-PCCA-2013-4-0614. D. Repovš was supported by the Slovenian Research Agency Grants P1-0292-0101, J1-6721-0101, J1-7025-0101 and J1-5435-0101.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, Athens, 15780, Greece

    Nikolaos S. Papageorgiou

  2. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Vicenţiu D. Rădulescu

  3. Department of Mathematics, University of Craiova, Street A.I. Cuza 13, 200585, Craiova, Romania

    Vicenţiu D. Rădulescu

  4. Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, Kardeljeva ploščad 16, 1000, Ljubljana, Slovenia

    Dušan D. Repovš

Authors
  1. Nikolaos S. Papageorgiou
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  2. Vicenţiu D. Rădulescu
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  3. Dušan D. Repovš
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Correspondence to Vicenţiu D. Rădulescu.

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Papageorgiou, N.S., Rădulescu, V.D. & Repovš, D.D. Nonlinear Elliptic Inclusions with Unilateral Constraint and Dependence on the Gradient. Appl Math Optim 78, 1–23 (2018). https://doi.org/10.1007/s00245-016-9392-y

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  • DOI: https://doi.org/10.1007/s00245-016-9392-y

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