Toronto Math Forum

APM346-2023S => APM346--Lectures & Home Assignments => Chapter 10 => Topic started by: Issra on April 01, 2023, 07:31:40 AM

Title: S 10.1 Lemma
Post by: Issra on April 01, 2023, 07:31:40 AM

Posted here since there is no section for Chapter 10.

In Lemma 1 in S10.1 (http://www.math.toronto.edu/ivrii/PDE-textbook/Chapter10/S10.1.html#:~:text=Lemma%201.,.%20Contradiction!), why is the condition $\phi(t_0) = \phi(t_1) = 0 $ necessary?

Title: Re: S 10.1 Lemma
Post by: Victor Ivrii on April 02, 2023, 05:15:13 AM

This condition is not necessary. However more conditions to $\phi$ lead to a lesser class of admissible $\phi$ in the assumption  and thus to weaker assumption of Lemma 1, and thus to stronger and more general statement.