1.* Let U C R? be an open and bounded set and u e C²(U) n C(U) satisfy -1 Ди(х) : in U. 1 + |x|
1.* Let U C R? be an open and bounded set and u e C²(U) n C(U) satisfy -1 Ди(х) : in U. 1 + |x|
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:1.* Let U c R? be an open and bounded set and u e C²(U) n C(U) satisfy
-1
Ди(х) —
in U.
1 + \x|
Show that u attains its minimum on the boundary of U. (Hint: Use a similar argument to the proof
of maximum principle for the heat equation on an interval and note that no auxiliary function v
is needed here.)
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