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Article summary:
1. The article discusses the continuation of solutions to elliptic and parabolic equations on hyperplanes, and provides conditional stability estimates for such solutions.
2. It applies the results to prove the uniqueness of an inverse source problem for a heat equation, and provides characterizations of hyperplanes that admit such continuation.
3. The article also discusses continuation for semi-linear elliptic equations.
Article analysis:
The article is well-written and presents its arguments in a clear and concise manner. The authors provide detailed explanations of their methods and results, as well as examples to illustrate their points. The article is also supported by relevant literature references, which adds to its credibility.
However, there are some potential biases in the article that should be noted. For example, the authors focus mainly on elliptic and parabolic equations limited on hyperplanes, without exploring other types of equations or boundary conditions that could be applicable in this context. Additionally, while they discuss semi-linear elliptic equations at the end of the paper, they do not provide any further details or examples to support their claims about these equations.
Furthermore, while the authors provide characterizations of hyperplanes that admit such continuation, they do not explore any counterarguments or alternative approaches that could be used instead. Additionally, they do not discuss any possible risks associated with using these methods or any potential limitations that could arise from them.
In conclusion, while this article is generally reliable and trustworthy due to its clear explanations and relevant literature references, it does have some potential biases that should be taken into consideration when evaluating its content.