Infinite-dimensional linear algebra and solvability of partial differential equations
| Autor: | Todor D. Todorov |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Partial differential equation Logic Weak solution 010102 general mathematics Space (mathematics) 01 natural sciences Mathematics - Analysis of PDEs Distribution (mathematics) Modeling and Simulation Primary: 15A03 35A01 35D35 35E20 35J15 46F05 46F10 47F05 Secondary: 46S20 46F30 Linear algebra FOS: Mathematics Partial derivative 0101 mathematics Algebraic number Analysis Analysis of PDEs (math.AP) Mathematics Vector space |
| Zdroj: | Journal of Logic and Analysis. 13 |
| ISSN: | 1759-9008 |
| Popis: | We discuss linear algebra of infinite-dimensional vector spaces in terms of algebraic (Hamel) bases. As an application we prove the surjectivity of a large class of linear partial differential operators with smooth ($\mathcal C^\infty$-coefficients) coefficients, called in the article \emph{regular}, acting on the algebraic dual $\mathcal D^*(\Omega)$ of the space of test-functions $\mathcal D(\Omega)$. The surjectivity of the partial differential operators guarantees solvability of the corresponding partial differential equations within $\mathcal D^*(\Omega)$. We discuss our result in contrast to and comparison with similar results about the restrictions of the regular operators on the space of Schwartz distribution $\mathcal D^\prime(\Omega)$, where these operators are often non-surjective. Comment: 34 pages |
| Databáze: | OpenAIRE |
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