Criterion for the functional dissipativity of the Lamé operator

After introducing the concept of functional dissipativity of the Dirichlet problem in a domain Ω⊂RN for systems of partial differential operators of the form ∂h(Ahk(x)∂k) (Ahk(x) being m×m matrices with complex valued L∞ entries), we find necessary and sufficient conditions for the functional dissipativity of the two-dimensional Lamé system. As an application of our theory we provide two regularity results for the displacement vector in the N-dimensional equilibrium problem, when the body is fixed along its boundary. © 2022

Authors
Cialdea A. 1 , Maz'ya V. 2, 3
Journal
European Journal of Mechanics, A/Solids
Publisher
Elsevier Ltd
Language
English
State
Published
Link
External link
DOI
10.1016/J.EUROMECHSOL.2022.104522
Number
104522
Year
2022
Organizations
  • 1 Department of Mathematics, Computer Sciences and Economics, University of Basilicata, V.le dell'Ateneo Lucano, 10, Potenza, 85100, Italy
  • 2 Department of Mathematics, Linköping University, Linköping, SE-581 83, Sweden
  • 3 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Keywords
Dissipativity; Lamé system
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