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Problem 5. Let N = {(x, y) E R² | 0 < y < 1- x²}, and define the divergence form operator Lu : = -(a"u;)j, 3 x2 + y (a“) = + Y 3 Prove that if Aı is the principal eigenvalue for the Dirichlet problem associated to L on N, in the weak sense, then A1 .

Problem 5. Let N = {(x, y) E R² | 0 < y < 1- x²}, and define the divergence form operator Lu : = -(a"u;)j, 3 x2 + y (a“) = + Y 3 Prove that if Aı is the principal eigenvalue for the Dirichlet problem associated to L on N, in the weak sense, then A1 .

Advanced Engineering Mathematics
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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Problem 5. Let N = {(x, y) E R² | 0 < y < 1– x²}, and define the divergence form operator Lu : = -(a³u;)j, x² + Y (a*) = (', *:") 3 x² + Y 3 Prove that if ı is the principal eigenvalue for the Dirichlet problem associated to L on N, in the weak sense, then A1 > 5. 1
Transcribed Image Text:Problem 5. Let N = {(x, y) E R² | 0 < y < 1– x²}, and define the divergence form operator Lu : = -(a³u;)j, x² + Y (a*) = (', *:") 3 x² + Y 3 Prove that if ı is the principal eigenvalue for the Dirichlet problem associated to L on N, in the weak sense, then A1 > 5. 1
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