On Subordination Conditions for Systems of Minimal Differential Operators

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On Subordination Conditions for Systems of Minimal Differential Operators. / Limanskiǐ, D.V.; Malamud, M.M.

In: Journal of Mathematical Sciences, Vol. 286, No. 1, 2024, p. 109-136.

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

Author

Limanskiǐ, D.V. ; Malamud, M.M. / On Subordination Conditions for Systems of Minimal Differential Operators. In: Journal of Mathematical Sciences. 2024 ; Vol. 286, No. 1. pp. 109-136.

BibTeX

@article{c634a7b5d3c84abfaa3449d4bedea8d7,

title = "On Subordination Conditions for Systems of Minimal Differential Operators",

abstract = "In this paper, we provide a review of results on a priori estimates for systems of minimal differential operators in the scale of spaces Lp(Ω), where p ∈ [1, ∞]. We present results on the characterization of elliptic and l-quasielliptic systems using a priori estimates in isotropic and anisotropic Sobolev spaces Wp,0lRn, p ∈ [1, ∞]. For a given set l = (l1,.., ln) ∈ Nn we prove criteria for the existence of l-quasielliptic and weakly coercive systems and indicate wide classes of weakly coercive in Wp,0lRn, p ∈ [1, ∞], nonelliptic, and nonquasielliptic systems. In addition, we describe linear spaces of operators that are subordinate in the L∞(Rn)-norm to the tensor product of two elliptic differential polynomials. {\textcopyright} 2024 Elsevier B.V., All rights reserved.",

keywords = "a priori estimate, coercivity, differential operator, quasiellipticity",

author = "D.V. Limanskiǐ and M.M. Malamud",

note = "Export Date: 01 November 2025; Cited By: 1; Correspondence Address: D.V. Limanskii; Donetsk State University, Donetsk, Russian Federation; email: d.limanskiy.dongu@mail.ru",

year = "2024",

doi = "10.1007/s10958-024-07493-3",

language = "English",

volume = "286",

pages = "109--136",

journal = "Journal of Mathematical Sciences (Switzerland)",

issn = "1072-3374",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - On Subordination Conditions for Systems of Minimal Differential Operators

AU - Limanskiǐ, D.V.

AU - Malamud, M.M.

N1 - Export Date: 01 November 2025; Cited By: 1; Correspondence Address: D.V. Limanskii; Donetsk State University, Donetsk, Russian Federation; email: d.limanskiy.dongu@mail.ru

PY - 2024

Y1 - 2024

N2 - In this paper, we provide a review of results on a priori estimates for systems of minimal differential operators in the scale of spaces Lp(Ω), where p ∈ [1, ∞]. We present results on the characterization of elliptic and l-quasielliptic systems using a priori estimates in isotropic and anisotropic Sobolev spaces Wp,0lRn, p ∈ [1, ∞]. For a given set l = (l1,.., ln) ∈ Nn we prove criteria for the existence of l-quasielliptic and weakly coercive systems and indicate wide classes of weakly coercive in Wp,0lRn, p ∈ [1, ∞], nonelliptic, and nonquasielliptic systems. In addition, we describe linear spaces of operators that are subordinate in the L∞(Rn)-norm to the tensor product of two elliptic differential polynomials. © 2024 Elsevier B.V., All rights reserved.

AB - In this paper, we provide a review of results on a priori estimates for systems of minimal differential operators in the scale of spaces Lp(Ω), where p ∈ [1, ∞]. We present results on the characterization of elliptic and l-quasielliptic systems using a priori estimates in isotropic and anisotropic Sobolev spaces Wp,0lRn, p ∈ [1, ∞]. For a given set l = (l1,.., ln) ∈ Nn we prove criteria for the existence of l-quasielliptic and weakly coercive systems and indicate wide classes of weakly coercive in Wp,0lRn, p ∈ [1, ∞], nonelliptic, and nonquasielliptic systems. In addition, we describe linear spaces of operators that are subordinate in the L∞(Rn)-norm to the tensor product of two elliptic differential polynomials. © 2024 Elsevier B.V., All rights reserved.

KW - a priori estimate

KW - coercivity

KW - differential operator

KW - quasiellipticity

U2 - 10.1007/s10958-024-07493-3

DO - 10.1007/s10958-024-07493-3

M3 - Article

VL - 286

SP - 109

EP - 136

JO - Journal of Mathematical Sciences (Switzerland)

JF - Journal of Mathematical Sciences (Switzerland)

SN - 1072-3374

IS - 1

ER -

ID: 143413585