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.
Brezis.Functional Analysis, Sobolev Spaces and Partial Differential Equations
7 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 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 pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.
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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Absolute continuity of generalized Wasserstein barycenters of finitely many measures
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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Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods
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.
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The Influence of Exclusion Zones on the Coexistence of Predator and Prey with an Allee Effect
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.
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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.
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Adversarial Robustness of NTK Neural Networks
NTK networks achieve minimax optimal adversarial regression rates in Sobolev spaces with early stopping, but minimum-norm interpolants are vulnerable.
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Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation
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.
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Well-posedness and regularity for seminlinear time-dependent second and fourth order in space equations
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.