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A Variational Approach for the Mixed Problem in the Elastostatics of Bodies with Dipolar Structure

  • Marin Marin
  • Vicenţiu Rădulescu
Open Access
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Abstract

In this study, we address the mixed initial boundary value problem in the elastostatics of dipolar bodies. Using the equilibrium equations, we build the operator of dipolar elasticity and prove that this operator is positively defined even in the general case of an elastic inhomogeneous and anisotropic dipolar solid. This helps us to prove the existence of a generalized solution for first boundary value problem and also the uniqueness of the solution. Moreover, relying on this property of the operator of dipolar elasticity to be positively defined, we can apply the known variational method proposed by Mikhlin.

Keywords

Dipolar bodies first boundary value problem operator of dipolar elasticity generalized solution variational method 

Mathematics Subject Classification

Primary 70G75 Secondary 53A45 58E30 74A20 

Notes

Acknowledgements

The authors are grateful to the anonymous reviewer for the careful reading of the initial version of this paper and for numerous suggestions that improved the present work. V.D. Rădulescu acknowledges the support through the Project MTM2017-85449-P of the DGISPI (Spain).

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTransilvania University of BraşovBrasovRomania
  2. 2.Faculty of Applied MathematicsAGH University of Science and TechnologyKrakówPoland
  3. 3.Department of MathematicsUniversity of CraiovaCraiovaRomania
  4. 4.Institute of Mathematics, Physics and MechanicsLjubljanaSlovenia

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