Lipschitz domain
View article: A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps
A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps Open
View article: The Cahill-Casazza-Daubechies problem on Hölder stable phase retrieval
The Cahill-Casazza-Daubechies problem on Hölder stable phase retrieval Open
Phase retrieval using a frame for a finite-dimensional Hilbert space is known to always be Lipschitz stable. However, phase retrieval using a frame or a continuous frame for an infinite-dimensional Hilbert space is always unstable. In orde…
View article: The Cahill-Casazza-Daubechies problem on Hölder stable phase retrieval
The Cahill-Casazza-Daubechies problem on Hölder stable phase retrieval Open
Phase retrieval using a frame for a finite-dimensional Hilbert space is known to always be Lipschitz stable. However, phase retrieval using a frame or a continuous frame for an infinite-dimensional Hilbert space is always unstable. In orde…
View article: The Lipschitz Liouville Property, Affine Rigidity, and Coarse Harmonic Coordinates on Groups of Polynomial Growth
The Lipschitz Liouville Property, Affine Rigidity, and Coarse Harmonic Coordinates on Groups of Polynomial Growth Open
We develop a quantitative theory of Lipschitz harmonic functions (LHF) on finitely generated groups, with emphasis on the Lipschitz Liouville property, affine rigidity, and quasi-isometric invariance for groups of polynomial growth. On fin…
View article: The Lipschitz Liouville Property, Affine Rigidity, and Coarse Harmonic Coordinates on Groups of Polynomial Growth
The Lipschitz Liouville Property, Affine Rigidity, and Coarse Harmonic Coordinates on Groups of Polynomial Growth Open
We develop a quantitative theory of Lipschitz harmonic functions (LHF) on finitely generated groups, with emphasis on the Lipschitz Liouville property, affine rigidity, and quasi-isometric invariance for groups of polynomial growth. On fin…
View article: Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth
Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth Open
For a fixed constant $λ> 0$ and a bounded Lipschitz domain $Ω\subset \mathbb{R}^n$ with $n \geq 2$, we establish that almost-minimizers (functions satisfying a sort of variational inequality) of the Alt-Caffarelli type functional \[ \mathc…
View article: Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth
Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth Open
For a fixed constant $λ> 0$ and a bounded Lipschitz domain $Ω\subset \mathbb{R}^n$ with $n \geq 2$, we establish that almost-minimizers (functions satisfying a sort of variational inequality) of the Alt-Caffarelli type functional \[ \mathc…
View article: Approximation property in terms of Lipschitz maps via tensor product approach
Approximation property in terms of Lipschitz maps via tensor product approach Open
This article explores the extension of the classical approximation property and its variants to the nonlinear framework of Lipschitz operator theory. Building on Grothendieck's tensor product methodology, we characterize the Lipschitz appr…
View article: Approximation property in terms of Lipschitz maps via tensor product approach
Approximation property in terms of Lipschitz maps via tensor product approach Open
This article explores the extension of the classical approximation property and its variants to the nonlinear framework of Lipschitz operator theory. Building on Grothendieck's tensor product methodology, we characterize the Lipschitz appr…
View article: Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise
Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise Open
In this article, we study the global well-posedness of hyperbolic SPDEs on a bounded domain in $\mathbb{R}^d$, driven by a space-time Lévy white noise, when the drift and diffusion coefficients are locally Lipschitz and have linear growth.…
View article: Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise
Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise Open
In this article, we study the global well-posedness of hyperbolic SPDEs on a bounded domain in $\mathbb{R}^d$, driven by a space-time Lévy white noise, when the drift and diffusion coefficients are locally Lipschitz and have linear growth.…
View article: Generalized Boundary Triples for Adjoint Pairs with Applications to Non-Self-Adjoint Schrödinger Operators
Generalized Boundary Triples for Adjoint Pairs with Applications to Non-Self-Adjoint Schrödinger Operators Open
We extend the notion of generalized boundary triples and their Weyl functions from extension theory of symmetric operators to adjoint pairs of operators, and we provide criteria on the boundary parameters to induce closed operators with a …
View article: On the differentiability of the value function of switched linear systems under arbitrary and controlled switching
On the differentiability of the value function of switched linear systems under arbitrary and controlled switching Open
This paper studies the differentiability of the value function of switched linear systems under arbitrary switching and controlled switching, referred to as worst-case and optimal value functions respectively. First, we show that the value…
View article: Lipschitz stability for a class of parametric optimization problems with polyhedral feasible set mapping
Lipschitz stability for a class of parametric optimization problems with polyhedral feasible set mapping Open
This paper is devoted to the Lipschitz analysis of the solution sets and optimal values for a class of parametric optimization problems involving a polyhedral feasible set mapping and a quadratic objective function with parametric linear p…
View article: On the differentiability of the value function of switched linear systems under arbitrary and controlled switching
On the differentiability of the value function of switched linear systems under arbitrary and controlled switching Open
This paper studies the differentiability of the value function of switched linear systems under arbitrary switching and controlled switching, referred to as worst-case and optimal value functions respectively. First, we show that the value…
View article: Well-posedness to nonlinear Schrödinger-Gerdjikov-Ivanon equation
Well-posedness to nonlinear Schrödinger-Gerdjikov-Ivanon equation Open
The Riemann-Hilbert approach is extended to discuss the well-posedness of the nonlinear Schrödinger-Gerdjikov-Ivanon equation. The Lipschitz continuity of potential in $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$ to scattering data is obtai…
View article: Well-posedness to nonlinear Schrödinger-Gerdjikov-Ivanon equation
Well-posedness to nonlinear Schrödinger-Gerdjikov-Ivanon equation Open
The Riemann-Hilbert approach is extended to discuss the well-posedness of the nonlinear Schrödinger-Gerdjikov-Ivanon equation. The Lipschitz continuity of potential in $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$ to scattering data is obtai…
View article: Extended Stokes Operators: Unifying Boundary-Bulk Relations in Non-Smooth Geometries
Extended Stokes Operators: Unifying Boundary-Bulk Relations in Non-Smooth Geometries Open
This paper introduces the concept of Extended Stokes Operators as a novel framework to address the challenges of fluid dynamics in non-smooth domains, such as those with Lipschitz or fractal boundaries. Classical formulations of the Stokes…
View article: Rademacher's Theorem in Metric Measure Spaces with No Doubling Condition
Rademacher's Theorem in Metric Measure Spaces with No Doubling Condition Open
This paper investigates the extension of Rademacher's theorem on the differentiability of Lipschitz functions to the setting of metric measure spaces that do not satisfy the doubling condition. The classical theorem and its initial general…
View article: Rademacher's Theorem in Metric Measure Spaces with No Doubling Condition
Rademacher's Theorem in Metric Measure Spaces with No Doubling Condition Open
This paper investigates the extension of Rademacher's theorem on the differentiability of Lipschitz functions to the setting of metric measure spaces that do not satisfy the doubling condition. The classical theorem and its initial general…
View article: Extended Stokes Operators: Unifying Boundary-Bulk Relations in Non-Smooth Geometries
Extended Stokes Operators: Unifying Boundary-Bulk Relations in Non-Smooth Geometries Open
This paper introduces the concept of Extended Stokes Operators as a novel framework to address the challenges of fluid dynamics in non-smooth domains, such as those with Lipschitz or fractal boundaries. Classical formulations of the Stokes…
View article: A-compact holomorphic Lipschitz mappings on the unit ball of a Banach space
A-compact holomorphic Lipschitz mappings on the unit ball of a Banach space Open
Let X and Y be complex Banach spaces, B_X be the open unit ball of X and HL(B_X,Y) be the Banach space of all holomorphic Lipschitz maps f:B_X->Y such that f(0)=0, endowed with the Lipschitz norm. Given a Banach operator ideal A, we use th…
View article: A-compact holomorphic Lipschitz mappings on the unit ball of a Banach space
A-compact holomorphic Lipschitz mappings on the unit ball of a Banach space Open
Let X and Y be complex Banach spaces, B_X be the open unit ball of X and HL(B_X,Y) be the Banach space of all holomorphic Lipschitz maps f:B_X->Y such that f(0)=0, endowed with the Lipschitz norm. Given a Banach operator ideal A, we use th…
View article: Near-optimal delta-convex estimation of Lipschitz functions
Near-optimal delta-convex estimation of Lipschitz functions Open
This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted reg…
View article: Near-optimal delta-convex estimation of Lipschitz functions
Near-optimal delta-convex estimation of Lipschitz functions Open
This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted reg…
View article: Lipschitz space with mixed logarithmic smoothness and embedding theorems
Lipschitz space with mixed logarithmic smoothness and embedding theorems Open
This article considers the Lipschitz space with mixed logarithmic smoothness of $2π$ periodic functions of several variables. We obtain equivalent descriptions of the norm of the Lipschitz space and prove embedding theorems between Besov a…
View article: Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian
Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian Open
Consider the Dirichlet-to-Neumann map $Λ_β$ associated with the Schrödinger operator $(D+β\A)^2$ with a magnetic potential in a bounded Lipschitz domain $Ω$, where $β>1$ is the field strength parameter. Assume that the magnetic field $\B=\…
View article: Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian
Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian Open
Consider the Dirichlet-to-Neumann map $Λ_β$ associated with the Schrödinger operator $(D+β\A)^2$ with a magnetic potential in a bounded Lipschitz domain $Ω$, where $β>1$ is the field strength parameter. Assume that the magnetic field $\B=\…
View article: Porosity of the free boundary in a class of higher-dimensional elliptic problems
Porosity of the free boundary in a class of higher-dimensional elliptic problems Open
We investigate a class of n -dimensional ( n\geq 2 ) free boundary elliptic problems, which includes the dam problem, the aluminum problem, and the lubrication problem. We establish that the free boundary in this class is a porous set, whi…
View article: Lipschitz space with mixed logarithmic smoothness and embedding theorems
Lipschitz space with mixed logarithmic smoothness and embedding theorems Open
This article considers the Lipschitz space with mixed logarithmic smoothness of $2π$ periodic functions of several variables. We obtain equivalent descriptions of the norm of the Lipschitz space and prove embedding theorems between Besov a…