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, …, 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.

Original languageEnglish
Pages (from-to)16-26
Number of pages11
JournalMathematical Notes of NEFU
Volume27
Issue number3
DOIs
Publication statusPublished - 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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