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

Durvudkhan Suragan; Nurgissa Yessirkegenov

doi:10.1007/s43036-021-00150-5

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

Durvudkhan Suragan
, Nurgissa Yessirkegenov

Ghent University
Al Farabi Kazakh National University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Article number	53
Journal	Advances in Operator Theory
Volume	6
Issue number	3
DOIs	https://doi.org/10.1007/s43036-021-00150-5
Publication status	Published - Jul 2021

Funding

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).

Keywords

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

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s43036-021-00150-5

Cite this

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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.",

keywords = "Anisotropic p-sub-Laplacian, Friedrichs inequality, Hardy inequality, p-sub-Laplacian, Picone{\textquoteright}s identity, Principal eigenvalue, Stratified group",

author = "Durvudkhan Suragan and Nurgissa Yessirkegenov",

note = "Funding Information: 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). Publisher Copyright: {\textcopyright} 2021, Tusi Mathematical Research Group (TMRG).",

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AU - Suragan, Durvudkhan

AU - Yessirkegenov, Nurgissa

N1 - Funding Information: 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). Publisher Copyright: © 2021, Tusi Mathematical Research Group (TMRG).

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N2 - 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.

AB - 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.

KW - Anisotropic p-sub-Laplacian

KW - Friedrichs inequality

KW - Hardy inequality

KW - p-sub-Laplacian

KW - Picone’s identity

KW - Principal eigenvalue

KW - Stratified group

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DO - 10.1007/s43036-021-00150-5

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VL - 6

JO - Advances in Operator Theory

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ER -

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

Abstract

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