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, Universitext, New York
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.
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.