Multiphase quadrature domains exist and are unique under sufficient conditions via constrained minimization of an energy functional over segregated states, with an example showing that energy minimization and partial balayage are not equivalent in the two-phase case.
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7 Pith papers cite this work, alongside 6,903 external citations. Polarity classification is still indexing.
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UNVERDICTED 7representative citing papers
NTK networks achieve minimax optimal adversarial regression rates in Sobolev spaces with early stopping, but minimum-norm interpolants are vulnerable.
Unique convex solutions exist for the second boundary value problem of mean curvature type equations with prescribed gradient image between uniformly convex bounded domains with smooth boundaries.
A PDE-based improvement-of-flatness technique for annuli provides an alternative proof of the end-structure and asymptotics for finite Morse index minimal hypersurfaces with Euclidean area growth in low dimensions.
A nonconforming virtual element method is developed for the vanishing moment approximation of the Monge-Ampère equation in 2D, with optimal a priori error estimates in H2, H1 and L2 norms plus existence and uniqueness of the discrete solution.
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.
The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.
citing papers explorer
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Multiphase quadrature domains (existence and uniqueness)
Multiphase quadrature domains exist and are unique under sufficient conditions via constrained minimization of an energy functional over segregated states, with an example showing that energy minimization and partial balayage are not equivalent in the two-phase case.
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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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The mean curvature type hypersurfaces with prescribed gradient image
Unique convex solutions exist for the second boundary value problem of mean curvature type equations with prescribed gradient image between uniformly convex bounded domains with smooth boundaries.
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Improvement of flatness in annuli
A PDE-based improvement-of-flatness technique for annuli provides an alternative proof of the end-structure and asymptotics for finite Morse index minimal hypersurfaces with Euclidean area growth in low dimensions.
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Nonconforming virtual element method for the Monge-Amp\`ere equation
A nonconforming virtual element method is developed for the vanishing moment approximation of the Monge-Ampère equation in 2D, with optimal a priori error estimates in H2, H1 and L2 norms plus existence and uniqueness of the discrete solution.
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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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Spectral properties of the Dirichlet-to-Neumann map for the Helmholtz equation
The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.