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 language | English |
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Pages (from-to) | 16-26 |
Number of pages | 11 |
Journal | Mathematical Notes of NEFU |
Volume | 27 |
Issue number | 3 |
DOIs | |
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