Problem 3. Integrate by parts to prove: [ 1 Dup de ≤ c ( √ lu² dx) * (√, 1D²ul² de) ³ for 2 < p ≤ ∞ and all u € W²P (U) WP(U). (Hint: Ju Du dr = Ei=1 Sy UzUz | Du-2 dr.)
Problem 3. Integrate by parts to prove: [ 1 Dup de ≤ c ( √ lu² dx) * (√, 1D²ul² de) ³ for 2 < p ≤ ∞ and all u € W²P (U) WP(U). (Hint: Ju Du dr = Ei=1 Sy UzUz | Du-2 dr.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 3.
Integrate by parts to prove:
√ (√√
Dup" de ≤ c lu² dr) ([\D²u/" de) +
dx
for 2 ≤ p ≤ ∞
and all u E W²P (U)
(Hint: Ju Du dx = Ei=1 Sv UzUx
WP (U).
| Dup-2 dr.)
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