Diierentiability of Statistical Experiments

Essentially Strictly Differentiable Lipschitz Functions

In this paper we address some of the most fundamental questions regarding the diierentiability structure of locally Lipschitz functions deened on Banach spaces. For example, we examine the relationship between inte-grability, D-representability and strict diierentiability. In addition to this, we show that on a large class of Banach spaces there is a signiicant family of locally Lipschitz funct...

On Differentiability of Metric Projections onto Moving Convex Sets

We consider properties of the metric projections onto moving convex sets in normed linear spaces. Under certain conditions about the norm, directional diierentiability (of higher order) of the metric projections at boundary points is characterized. The characterization is formulated in terms diierentiability of multifunctions and properties of the set-derivatives are shown.

Fractional Order Diierentiability of the Gradient of Solutions to Elliptic Equations with Mixed Boundary Conditions

Fréchet Differentiability of the Solution of the Heat Equation With Respect to a Nonlinear Boundary Condition

Fr echet diierentiability of the solution of the heat equation with respect to a nonlinear boundary condition Arnd RR osch Abstract. Consider the heat equation with a nonlinear function in the boundary condition which depends only on the boundary values x of the solution u of the initial-boundary value problem. The function belongs to a set of admissible diierentiable or uniformly Lipschitz con...

Diierentiability of Solutions of an Electro-elasticity Model W.r.t. Parameters

A model describing a linear thin plate exited by a piezoelectric patch is considered. The peculiarity of this model consists in the presence of an unbounded input operator on the right-hand-side of the model's equation. The main purpose of the paper is to prove the existence of derivatives of solutions with respect to parameters. Such a diierentiability is proved for an appropriate space, which...