On the extension of Lipschitz, Lipschitz-Hölder continuous, and monotone functions

On the Extension of Lipschitz, Lipschitz- Hölder Continuous, and Monotone Functions

Extension of P-adic Definable Lipschitz Functions

Write OK for the valuation ting, MK for the maximal ideal of K and kK for the residue field. Let us fix $ some uniformizer of K. We denote by acm : K → OK/(MK) the map sending some nonzero x ∈ K to x$−ord(x) mod MK , and sending zero to zero. This is a definable map. We denote by RV the union of K×/(1 +MK) and {0} and by rv : K → RV the quotient map. More generally, if m ∈ N∗, we set RVm = K×/(...

Definable Smoothing of Lipschitz Continuous Functions

Let M be an o-minimal structure over the real closed field R. We prove the definable smoothing of definable Lipschitz continuous functions. In the case of Lipschitz functions of one variable we are even able to preserve the Lipschitz constant.

Analyticity of Dirichlet-Neumann Operators on Hölder and Lipschitz Domains

In this paper we take up the question of analyticity properties of Dirichlet–Neumann operators with respect to boundary deformations. In two separate results, we show that if the deformation is sufficiently small and lies either in the class of C1+α (any α > 0) or Lipschitz functions, then the Dirichlet–Neumann operator is analytic with respect to this deformation. The proofs of both results ut...

Lipschitz and Hölder stability of optimization problems and generalized equations

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper Hölder type, respectively, hold. Furthermore, we apply the ...