Integrate by parts to prove: ≤C : © (√₁ \u² dz)* (/[\D²u³² dz) ³ [\Dup de (/ for 2 < p ≤ ∞ and all u € W²²(U) WP (U). p-2 (Hint: Ju Du dx = Σ₁=1 Sv UzUz, | Du|P-² d.x.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 3.
Integrate by parts to prove:
[\Du" dr ≤ c ( \u² dr) ³ ( [\D²u/" da) *
C
14²
U
for 2 < p ≤ ∞
(Hint: Jy |Du
and all u € W²P (U) WP(U).
dx = Σ₁=1 Sv U₁₁Ux₁ |Du/²-2 d.x.)
Transcribed Image Text:Problem 3. Integrate by parts to prove: [\Du" dr ≤ c ( \u² dr) ³ ( [\D²u/" da) * C 14² U for 2 < p ≤ ∞ (Hint: Jy |Du and all u € W²P (U) WP(U). dx = Σ₁=1 Sv U₁₁Ux₁ |Du/²-2 d.x.)
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