Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
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Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations
10 Pith papers cite this work. Polarity classification is still indexing.
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Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.
A predator-prey reaction-diffusion model with Allee effect and exclusion zones admits positive coexistence equilibria when the predator-free area is sufficiently large, proven globally via topological degree theory, with non-vanishing predator populations as the predation area shrinks.
A prox-based semi-smooth Newton method for TV-minimization that is globally well-posed and locally superlinearly convergent under finite element discretization, extending to broader convex problems.
A convection-diffusion model with sparsity-regularized Radon measure source recovers point gas leak locations and intensities from concentration measurements while jointly estimating convection and diffusion parameters.
NTK networks achieve minimax optimal adversarial regression rates in Sobolev spaces with early stopping, but minimum-norm interpolants are vulnerable.
A decoupled kernel-only stabilization for finite-strain VEM hyperelasticity is introduced that scales deviatoric terms by shear modulus with geometry weights and volumetric terms independently by bulk modulus, with uniform stability proven under polygon regularity.
A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.
GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.
Existence and uniqueness of weak solutions are proved for the semilinear time-dependent equation with second or fourth order diffusion and cubic nonlinearity, for both smooth and rough initial data via Faedo-Galerkin and compactness methods.
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Leak localisation with a measure source convection-diffusion model
A convection-diffusion model with sparsity-regularized Radon measure source recovers point gas leak locations and intensities from concentration measurements while jointly estimating convection and diffusion parameters.