9.2.10. Let L = D². Using the L2 inner products on both the domain and target spaces, write down a set of homogeneous boundary conditions that makes L* D². Then set S = L* L = D. Do your boundary conditions lead to a boundary value problem S[u] f that is (i) positive definite; (ii) positive semi-definite; or (iii) neither? = =

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9.2.10. Let L = D². Using the L² inner products on both the domain and target spaces,
D². Then set
write down a set of homogeneous boundary conditions that makes L*
S = L* L = D¹. Do your boundary conditions lead to a boundary value problem
f that is (i) positive definite; (ii) positive semi-definite; or (iii) neither?
S[u]
=
=
Transcribed Image Text:9.2.10. Let L = D². Using the L² inner products on both the domain and target spaces, D². Then set write down a set of homogeneous boundary conditions that makes L* S = L* L = D¹. Do your boundary conditions lead to a boundary value problem f that is (i) positive definite; (ii) positive semi-definite; or (iii) neither? S[u] = =
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