Boundary value problems for third–order pseudoelliptic equations with degeneration

Aleksandr I. Kozhanov

doi:10.25587/SVFU.2020.63.12.002

Boundary value problems for third–order pseudoelliptic equations with degeneration

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Abstract

We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations (Formula Presented) x ∈ Ω ⊂ ℝⁿ, t ∈ (0, T), where ∆ if the Laplace operator acting in the variables x₁, …, x_n and B is a second-order elliptic operator acting in the same variables x₁, …, x_n. A fea-ture of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev’s deriva-tives in the equation) are proved for the problems under study.

Original language	English
Pages (from-to)	16-26
Number of pages	11
Journal	Mathematical Notes of NEFU
Volume	27
Issue number	3
DOIs	https://doi.org/10.25587/SVFU.2020.63.12.002
Publication status	Published - 2020

Keywords

Degeneration
Elliptic boundary value problem
Existence
Regular solution
Third-order differential equation
Uniqueness

OECD FOS+WOS

1.02 COMPUTER AND INFORMATION SCIENCES
1.01 MATHEMATICS

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10.25587/SVFU.2020.63.12.002

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title = "Boundary value problems for third–order pseudoelliptic equations with degeneration",

abstract = "We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations (Formula Presented) x ∈ Ω ⊂ ℝn, t ∈ (0, T), where ∆ if the Laplace operator acting in the variables x1, …, xn and B is a second-order elliptic operator acting in the same variables x1, …, xn. A fea-ture of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev{\textquoteright}s deriva-tives in the equation) are proved for the problems under study.",

keywords = "Degeneration, Elliptic boundary value problem, Existence, Regular solution, Third-order differential equation, Uniqueness",

author = "Kozhanov, {Aleksandr I.}",

year = "2020",

doi = "10.25587/SVFU.2020.63.12.002",

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AU - Kozhanov, Aleksandr I.

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N2 - We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations (Formula Presented) x ∈ Ω ⊂ ℝn, t ∈ (0, T), where ∆ if the Laplace operator acting in the variables x1, …, xn and B is a second-order elliptic operator acting in the same variables x1, …, xn. A fea-ture of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev’s deriva-tives in the equation) are proved for the problems under study.

AB - We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations (Formula Presented) x ∈ Ω ⊂ ℝn, t ∈ (0, T), where ∆ if the Laplace operator acting in the variables x1, …, xn and B is a second-order elliptic operator acting in the same variables x1, …, xn. A fea-ture of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev’s deriva-tives in the equation) are proved for the problems under study.

KW - Degeneration

KW - Elliptic boundary value problem

KW - Existence

KW - Regular solution

KW - Third-order differential equation

KW - Uniqueness

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SP - 16

EP - 26

JO - Математические заметки СВФУ

JF - Математические заметки СВФУ

SN - 2411-9326

IS - 3

ER -

Boundary value problems for third–order pseudoelliptic equations with degeneration

Abstract

Keywords

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