Optimal constants for a nonlocal approximation of Sobolev norms and total variation

Circulation integrals and critical Sobolev spaces : problems of optimal constants

We study various questions related to the best constants in the following inequalities established in [1, 2, 3]; ̨̨̨Z Γ ~ φ · ~t ̨̨̨ ≤ Cn‖∇φ‖Ln |Γ| , and ̨̨̨Z Rn ~ φ · ~ μ ̨̨̨ ≤ Cn‖∇φ‖Ln‖~ μ‖ , where Γ is a closed curve in Rn, ~ φ ∈ C∞ c (Rn; Rn) and ~ μ is a bounded measure on Rn with values into Rn such that div ~ μ = 0. In 2d the answers are rather complete and closely related to the best constants for ...

Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions

We prove that the best constant for the critical embedding of higher order Sobolev spaces does not depend on all the traces. The proof uses a comparison principle due to Talenti [19] and an extension argument which enables us to extend radial functions from the ball to the whole space with no increase of the Dirichlet norm. Similar arguments may also be used to prove the very same result for Ha...

a benchmarking approach to optimal asset allocation for insurers and pension funds

uncertainty in the financial market will be driven by underlying brownian motions, while the assets are assumed to be general stochastic processes adapted to the filtration of the brownian motions. the goal of this study is to calculate the accumulated wealth in order to optimize the expected terminal value using a suitable utility function. this thesis introduced the lim-wong’s benchmark fun...

Optimal Sobolev Norms and the L Minkowski Problem

Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

Hyperspectral image (HSI) possesses three intrinsic characteristics: the global correlation across spectral domain, the nonlocal self-similarity across spatial domain, and the local smooth structure across both spatial and spectral domains. This paper proposes a novel tensor based approach to handle the problem of HSI spatial super-resolution by modeling such three underlying characteristics. S...