Elliptic Functional Differential Equations with Contractions and Extensions of Independent Variables of the Unknown Function

Rossovskii, L. E.

doi:10.1007/s10958-017-3360-1

Cited by 33 publications

(30 citation statements)

References 41 publications

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“…(i.e., only contractions of independent variables are allowed), where Ω is a bounded domain in R n such that its boundary is smooth and Ω ⊂ qΩ, the coefficients a jα (x) are smooth in Ω, and T j (x, D) are differential operators with smooth in ∂Ω coefficients. The main results (obtained in [63], Chap. 3) are as follows:…”

Section: Higher-order Equations Problems In Weighted Spaces and Spementioning

confidence: 97%

“…First, the problem to find algebraic conditions guaranteeing the strong ellipticity of the investigated equation (the coercivity problem) is solved. For the case of constant coefficients of the operators R αβ , the result is as follows (see [63], Sect. 2.1).…”

Section: Strong Elliptic Operators and Equationsmentioning

confidence: 98%

“…A thorough and comprehensive explanation of the current state of the above theory is provided in [63].…”

Section: Functional-differential Equations With Contractions and Extementioning

confidence: 99%

“…In Chapter 2 of [63], the general Dirichlet problem 11) under the assumption that equation (6.10) is strongly elliptic, the operators R αβ act according to the relation…”

Section: Strong Elliptic Operators and Equationsmentioning

confidence: 99%

“…For the case of constant coefficients, the smoothness of generalized solutions increases (see [63], Sect. 2.4).…”

Section: Introduce the Unbounded Operatormentioning

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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Section: Higher-order Equations Problems In Weighted Spaces and Spementioning

confidence: 97%

Section: Strong Elliptic Operators and Equationsmentioning

confidence: 98%

“…A thorough and comprehensive explanation of the current state of the above theory is provided in [63].…”

Section: Functional-differential Equations With Contractions and Extementioning

confidence: 99%

“…In Chapter 2 of [63], the general Dirichlet problem 11) under the assumption that equation (6.10) is strongly elliptic, the operators R αβ act according to the relation…”

Section: Strong Elliptic Operators and Equationsmentioning

confidence: 99%

“…For the case of constant coefficients, the smoothness of generalized solutions increases (see [63], Sect. 2.4).…”

Section: Introduce the Unbounded Operatormentioning

confidence: 99%

See 3 more Smart Citations