w on ƏN and cos (|Du[²))ui + u(|Du|³ + 1) < –(2- :- cos (|Dw[?))wii+ w(|Dw|3 + 1) i=1 en u < w on all of N.
w on ƏN and cos (|Du[²))ui + u(|Du|³ + 1) < –(2- :- cos (|Dw[?))wii+ w(|Dw|3 + 1) i=1 en u < w on all of N.
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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3
Transcribed Image Text:Problem 4. Let N C R" be an open domain. Prove that if u, w E C²(N) N C'(N) are such
that u < w on ƏN and
n
n
(2
- cos (|Dul?))ui + u(|Du|³ + 1) <-(2 – cos (|Dw?))Wii + w(|Dw|°+ 1)
i=1
i=1
on N, then u<w on all of N.
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