Related papers: On higher Lipschitz invariants

In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family of parameterized ``split" feasibility…

We study the well-posedness and the long-time behavior of almost periodic solutions to stochastic degenerate parabolic-hyperbolic equations in any space dimension, under the assumption of Lipschitz continuity of the flux and viscosity…

A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…

In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…

We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.

In this paper, we extend the method of invariant sets of descending flow that proposed by Sun Jingxian for smooth functionals to the locally Lipschitz functionals. By this way, we obtain the existence results for the positive, negative and…

In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…

In this note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier \cite{BorgesZeMarcio}. As in the theory of functions of a complex variable, it is expected that…

We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…

We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.

We define Hardy classes of bicomplex-valued functions on the complex unit disk which solve bicomplex versions of the Beltrami and related equations. Using representations in terms of their complex-valued counterparts, we show these…

We establish sharp lower bounds for shifted (with two shifts) moments of Dirichlet $L$-function of fixed modulus under the generalized Riemann hypothesis.

In this work we prove a new $L^p$ holomorphic extension result for functions defined on product Lipschitz surfaces with small Lipschitz constants in two complex variables. We define biparameter and partial Cauchy integral operators that…

Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.

Functions that are holomorphic and Lipschitz in a smoothly bounded domain enjoy a gain in the order of Lipschitz regularity in the complex tangential directions near the boundary. We describe this gain explicitly in terms of the defining…

This object of this paper to give several properties and applications of multiple p-adic q-L-function of two variables.

We develop a new approach to the invertibility of the layer potentials on $L^p$ associated with elliptic equations and systems in Lipschitz domains. As a consequence, for $n\ge 4$ and $(2(n-1)/(n+1))-\epsilon<p<2$, we obtain the solvability…

We give partial answers to a metric version of Zariski's multiplicity conjecture. In particular, we prove the multiplicity of complex analytic surface (not necessarily isolated) singularities in $\mathbb{C}^3$ is a bi-Lipschitz invariant.

We propose a new method to apply the Lipschitz functional calculus of local Dirichlet forms to Poisson random measures.

First we prove a Littlewood-Paley diagonalization result for bi-Lipschitz perturbations of the identity map on the real line. This result entails a number of corollaries for the Hilbert transform along lines and monomial curves in the…