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Fisher–Rao geometry of equivalent Gaussian measures on infinite-dimensional Hilbert spaces
This work presents an explicit description of the Fisher–Rao Riemannian metric on the Hilbert manifold of equivalent centered Gaussian measures on an...
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Fiberwise Symmetrizations for Variational Problems on Fibred Manifolds
We establish a framework for fiberwise symmetrization to find a lower bound of a Dirichlet-type energy functional in a variational problem on a...
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Decay and Global Well-Posedness of the Free-Boundary Incompressible Euler Equations with Dam**
We consider the free boundary problem for a layer of incompressible fluid lying below the atmosphere and above a rigid bottom in the horizontally...
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On the Energy Equality via a Priori Bound on the Velocity for Axisymmetric 3D Navier–Stokes Equations
In this paper, we are concerned with the energy equality for axisymmetric weak solutions of the 3D Navier–Stokes equations. The classical Shinbrot...
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A historical perspective on Schützenberger-Pinsker inequalities (extended version)
This paper presents a tutorial overview of so-called Pinsker inequalities which establish a precise relationship between information and statistics,...
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Harmonic and Monogenic Functions on Toroidal Domains
A standard technique for producing monogenic functions is to apply the adjoint quaternionic Fueter operator to harmonic functions. We will show that...
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Shape Gradient Methods for Shape Optimization of an Unsteady Multiscale Fluid–Structure Interaction Model
We consider numerical shape optimization of a fluid–structure interaction model. The constrained system involves multiscale coupling of a...
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A General Integral Identity with Applications to a Reverse Serrin Problem
We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with...
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Demiclosed principle and some fixed-point theorems for generalized nonexpansive map**s in Banach spaces
The aim of this paper is to discuss some results concerning the demiclosedness principle of generalized, nonexpansive map**s in uniformly convex...
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Global Dynamics of 3D Compressible Viscous and Heat-Conducting Micropolar Fluids with Vacuum at Infinity
In this paper, we are concerned with the Cauchy problem of 3D viscous and heat-conducting micropolar fluids with far field vacuum. Compared with the...
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Top degree \(\ell ^p\)-homology and conformal dimension of buildings
For a non-compact finite thickness building whose Davis apartment is an orientable pseudomanifold, we compute the supremum of the set of
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