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Free scalar field theory on a Sobolev space over a bounded interval
This paper discusses several functional analytic issues relevant for field theories in the context of the Hamiltonian formulation for a free,...
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Global Existence of Non-Cutoff Boltzmann Equation in Weighted Sobolev Space
This article presents a new approach of semigroup analysis and pseudo-differential calculus for deriving the regularizing estimate on non-cutoff...
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Endpoint Sobolev Theory for the Muskat Equation
This paper is devoted to the study of solutions with critical regularity for the two-dimensional Muskat equation. We prove that the Cauchy problem is...
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Quantum Gaussian maximizers and log-Sobolev inequalities
In the present paper, we give a proof of optimality of Gaussian encodings for the ultimate communication rate of generalized noisy homodyne and...
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Stability of Logarithmic Sobolev Inequalities Under a Noncommutative Change of Measure
We generalize Holley–Stroock’s perturbation argument from commutative to finite dimensional quantum Markov semigroups. As a consequence, results on...
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Phase Transitions, Logarithmic Sobolev Inequalities, and Uniform-in-Time Propagation of Chaos for Weakly Interacting Diffusions
In this article, we study the mean field limit of weakly interacting diffusions for confining and interaction potentials that are not necessarily...
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Interpolation Between Modified Logarithmic Sobolev and Poincaré Inequalities for Quantum Markovian Dynamics
We define the quantum p -divergence and introduce Beckner’s inequalities for primitive quantum Markov semigroups on a finite-dimensional matrix...
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Euler–Lagrangian Approach to Stochastic Euler Equations in Sobolev Spaces
The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler...
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Bounds for the Kolmogorov Widths of the Sobolev Weighted Classes with Conditions on the Zero and Highest Derivatives
AbstractIn this paper, order estimates for the Kolmogorov widths of sets defined by restrictions on the norm in the Sobolev weighted space
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Hypercontractivity and Logarithmic Sobolev Inequality for Non-primitive Quantum Markov Semigroups and Estimation of Decoherence Rates
We generalize the concepts of weak quantum logarithmic Sobolev inequality (LSI) and weak hypercontractivity (HC), introduced in the quantum setting...
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A study on single-iteration sobolev descent for linear initial value problems
Mahavier and Montgomery construct a Sobolev space for approximate solution of linear initial value problems in a finite difference setting in...
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Non-linear Log-Sobolev Inequalities for the Potts Semigroup and Applications to Reconstruction Problems
Consider the semigroup of random walk on a complete graph, which we call the Potts semigroup. Diaconis and Saloff-Coste (Ann Appl Probab...
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Convergence in \(\mathcal {L}(L^2)\) for Potentials in Kato-Sobolev Spaces
The goal of this chapter is to derive convergence results in the L2 operator norm for a standard family of time-slicing approximations introduced by...
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Sobolev Gradients for the Möbius Energy
Aiming to optimize the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary...
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Nonlinear Asymptotic Stability and Transition Threshold for 2D Taylor–Couette Flows in Sobolev Spaces
In this paper, we investigate the stability of the 2-dimensional (2D) Taylor–Couette (TC) flow for the incompressible Navier–Stokes equations. The...
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Space-Time Fluctuations in a Quasi-static Limit
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit....