Showing papers by "Juliette Leblond published in 1999"
TL;DR: In this paper, a family of inverse problems for the 2D Laplacian related to non-destructive testing is introduced. But the complexity of the inverse problem is not the same as that of approximation theory in the complex domain.
Abstract: We exhibit new links between approximation theory in the complex domain and a family of inverse problems for the 2D Laplacian related to non-destructive testing.
53 citations
TL;DR: In this paper, the authors consider a family of bounded extremal problems and interpolation problems expressed using two distinct orthogonal decomposi-tions of some Hilbert space and show that these problems can be expressed in terms of Hilbert space optimization.
17 citations
TL;DR: In this paper, the authors studied the shortest plane paths joining two given points with given tangent angles and curvatures along which the tangent angle and the curvature are continuous and the derivative of the curvatures is bounded.
Abstract: We study the shortest plane paths joining two given points with given tangent angles and curvatures along which the tangent angle and the curvature are continuous and the derivative of the curvature is bounded. At a point where such a path is of class C3, it must be locally a piece of a clothoid or a line segment (up to an isometry, a clothoid is given by Fresnel's integrals x(t) = ∝0t cos τ2 dτ, y(t) = ∝0t sin τ2 dτ, where t is the arc length). We prove that if the distance between its initial and final points is large enough, then a generic shortest path contains infinitely many switching points.
4 citations