Elliptic differential‐difference operators with degeneration and the Kato square root problem

Скубачевский, А. Л.

doi:10.1002/mana.201700475

Cited by 14 publications

(4 citation statements)

References 26 publications

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“…[77,78], and references therein). The current state of the functional-differential theory can be characterized by the following main results (obtained in [77][78][79]).…”

Section: Kato Square Root Problemmentioning

confidence: 99%

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Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

Muravnik

2019

Math. Model. Nat. Phenom.

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This paper presents a review of results on nonlocal problems, functional-differential equations, and their applications, obtained during several last years. The following research areas are covered: the Kato square root problem for functional-differential operators, Vlasov equations and their applications to the modelling of high-temperature plasma, specific properties of differential-difference equations with incommensurable translations, degenerate functional-differential equations and their applications, functional-differential equations with contractions and extensions of independent variables, and operational methods for parabolic and elliptic functional-differential equations.

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“…[77,78], and references therein). The current state of the functional-differential theory can be characterized by the following main results (obtained in [77][78][79]).…”

Section: Kato Square Root Problemmentioning

confidence: 99%

“…The Kato property of elliptic differential-difference operators degenerated in cylindrical domains is one of the most recent results obtained in the considered research area (see [79]). On the other hand, it is quite convenient for the demonstration of specific effects arising in more general cases.…”

Section: Kato Problem For Operators Degenerated In Cylindersmentioning

confidence: 99%

Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

Muravnik

2019

Math. Model. Nat. Phenom.

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“…Skubachevskii and scientists around him. Here, we first of all mention the book [1] and some recent papers [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] (see also the references therein). A nice survey of previous results, including ones by other authors, as well as a survey of results on ordinary differential equations with delays are given in book [1] and paper [2].…”

Section: Introductionmentioning

confidence: 99%

Resolvent Convergence for Differential–Difference Operators with Small Variable Translations

Borisov,

Polyakov

2023

Mathematics

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We consider general higher-order matrix elliptic differential–difference operators in arbitrary domains with small variable translations in lower-order terms. The operators are introduced by means of general higher-order quadratic forms on arbitrary domains. Each lower-order term depends on its own translation and all translations are governed by a small multi-dimensional parameter. The operators are considered either on the entire space or an arbitrary multi-dimensional domain with a regular boundary. The boundary conditions are also arbitrary and general and involve small variable translations. Our main results state that the considered operators converge in the norm resolvent sense to ones with zero translations in the best possible operator norm. Estimates for the convergence rates are established as well. We also prove the convergence of the spectra and pseudospectra.

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“…. It is proved in [16, Theorem 1] that the operator G is maximal accretive and the equality dom B The Kato problem was positively solved in [13] for a class of abstract maximal sectorial operators, in [7,8,6,9,10,24] for elliptic differential operators, in [30,31] for some class of strongly elliptic functional-differential operators.…”

Section: Introductionmentioning

confidence: 99%

On the Kato square root problem

Arlinskii̇̆¹

2021

Preprint

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Elliptic differential‐difference operators with degeneration and the Kato square root problem

Abstract: We prove correctness of the Kato square root conjecture for elliptic differential‐difference operators with degeneration.

Cited by 14 publications

References 26 publications

Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

Resolvent Convergence for Differential–Difference Operators with Small Variable Translations

On the Kato square root problem

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