Math 442: Intro to Partial Differential Equations Homework 6
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Homework 6
Math 442: Intro to Partial Differential Equations
(Exercises are taken from Partial Differential Equations An Introduction, Second Edition by Walter A. Strauss.)
1. Exercise §5.5 #3. Prove the inequality l R 0 l (f 0 (x))2dx ≥ [f(l) − f(0)]2 for any real function f(x) whose derivative f ’(x) is continuous. [Hint: Use Schwarz’s inequality with the pair f ’(x) and 1.]
2. Exercise §5.5 #8. Prove that both integrals in (12) tend to zero.
2023-07-24