The Bend of Bernstein Polynomials.
The H–1-norm of tubular neighbourhoods of curves
We study the H–1-norm of the function 1 on tubular neighbourhoods of curves in . We take the limit of small thicknessε, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit ε → 0, containing contributions from the length of the curve (at order ε3), the ends (ε4), and the curvature (ε5). The second result is a Γ-convergence result, in which the central curve may vary along the sequence ε → 0. We prove that a rescaled version of the...
The H–1-norm of tubular neighbourhoods of curves
We study the H–1-norm of the function 1 on tubular neighbourhoods of curves in . We take the limit of small thickness ε, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit ε → 0, containing contributions from the length of the curve (at order ε3), the ends (ε4), and the curvature (ε5). The second result is a Γ-convergence result, in which the central curve may vary along the sequence ε → 0. We prove that a rescaled version of...
The Lagrange complex
The Plateau Problem for Surfaces of Prescribed Mean Curvature in a Cylinder.
Title: Solution in large of control problem