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Register a new usersup+inf for Riemannian surfaces and sup*inf for for bounded domains of R^n, n>2
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Authors
Samy Skander Bahoura
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This paper is in relation with a Note of Comptes Rendus de lAcademie des Sciences 2005. We have an idea about a lower bounds of sup+inf (2 dimensions) and sup*inf (dimensions >2).
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We prove an a priori estimate of type sup*inf on Riemannian manifold of dimension 3 (not necessarily compact).
We give a sup+inf inequality on $S_4$ for Paneitz operator.
We give a derivation for the value of inf-sup constant for the bilinear form (p, div u). We prove that the value of inf-sup constant is equal to 1.0 in all cases and is independent of the size and shape of the domain. Numerical tests for validation of inf-sup constants is performed using finite dimensional spaces defined in cite{2020jain} on two test domains i) a square of size $Omega = [0,1]^2$, ii) a square of size $Omega = [0,2]^2$, for varying mesh sizes and polynomial degrees. The numeric values are in agreement with the theoretical value of inf-sup term.
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