A Runge theorem for solutions of the heat equation
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- by R. Diaz PDF
- Proc. Amer. Math. Soc. 80 (1980), 643-646 Request permission
Abstract:
Let ${\Omega _1}$ and ${\Omega _2}$ be open sets in ${R^n}$ such that ${\Omega _1} \subset {\Omega _2}$. Every solution of the heat equation on ${\Omega _1}$ admits approximation on the compact subsets of ${\Omega _1}$ by functions which satisfy the heat equation throughout ${\Omega _2}$ if and only if this topological condition is met: For every hyperplane $\pi$ in ${R^n}$ orthogonal to the time axis, every compact component of $\pi \backslash {\Omega _1}$ contains a compact component of $\pi \backslash {\Omega _2}$.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 643-646
- MSC: Primary 35K05; Secondary 31B35, 35E20
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587944-2
- MathSciNet review: 587944