Generalised nonlinear Picone identities for p-sub-Laplacians and p-biharmonic operators and applications

Abstract

In this paper, we establish generalised nonlinear Picone identities for p-sub-Laplacians, anisotropic p-sub-Laplacians and p-biharmonic operators on general stratified Lie groups. Moreover, we give applications to horizontal Hardy inequalities, Sturmian comparison principles as well as to weighted eigenvalue problems for p-sub-Laplacian and p-biharmonic operators.

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Acknowledgements

This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant no. AP09057887). The authors were supported by the Nazarbayev University Program 091019CRP2120. The second author was also supported by the FWO Odysseus 1 Grant G.0H94.18N: Analysis and Partial Differential Equations and the Ministry of Education and Science of the Republic of Kazakhstan (Grant no. AP09058474).

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Correspondence to Nurgissa Yessirkegenov.

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Communicated by Daniel Pellegrino.

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Suragan, D., Yessirkegenov, N. Generalised nonlinear Picone identities for p-sub-Laplacians and p-biharmonic operators and applications. Adv. Oper. Theory 6, 53 (2021). https://doi.org/10.1007/s43036-021-00150-5

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Keywords

  • Picone’s identity
  • p-sub-Laplacian
  • Anisotropic p-sub-Laplacian
  • Hardy inequality
  • Friedrichs inequality
  • Stratified group
  • Principal eigenvalue

Mathematics Subject Classification

  • 35A23
  • 35H20
  • 35P30