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Moduli spaces of polygons and deformations of polyhedra with boundary
We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the...
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Nonstandard Boundary Conditions
In this Chapter, we study three variants of the least gradient problem related to the shape of the domain. The first one concerns the case when we...
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Boundary values of pluriharmonic functions with Bott-Chern cohomology
The main purpose of this paper is to investigate the relationship between continuation of pluriharmonic functions from the boundary of an unbounded...
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Navier–Stokes Equations with Regularized Directional Boundary Condition
We consider the steady Navier–Stokes equations in a bounded domain...
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Generalized Boundary Integral Equation Method for Boundary Value Problems of Two-D Isotropic Lattice Laplacian
A generalized boundary integral equation method for boundary value problems of two-dimensional isotropic lattice Laplacian is proposed in this paper....
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Characteristic Equations for True and Fictitious Eigenvalues of Muller Boundary Integral Equations
AbstractThe paper is devoted to the mathematical modelling of two-dimensional microcavity lasers. Using the Galerkin method with trigonometric basis,...
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Why Boundary Regularity?
In this chapter we present some classical results in several complex variables that relate boundary smoothness of domains with the geometric...
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On a Countable Family of Boundary Graph Classes for the Dominating Set Problem
AbstractA hereditary class is a set of simple graphs closed under deletion of vertices; every such class is defined by the set of its minimal...
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Failure-Informed Adaptive Sampling for PINNs, Part II: Combining with Re-sampling and Subset Simulation
This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks (PINNs). In our previous work...
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Boundary Rigidity, and Non-Rigidity, of Projective Structures
We investigate the property of boundary rigidity for the projective structures associated to torsion-free affine connections on connected smooth...
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Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition
In this paper, we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the...
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A Prescribed Scalar and Boundary Mean Curvature Problem and the Yamabe Classification on Asymptotically Euclidean Manifolds with Inner Boundary
We consider the problem of finding a metric in a given conformal class with prescribed non-positive scalar curvature and non-positive boundary mean...
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Asymptotic Analysis of Boundary-Value Problems for the Laplace Operator with Frequently Alternating Type of Boundary Conditions
This work, which can be considered as a small monograph, is devoted to the study of two-and three-dimensional boundary-value problems for eigenvalues...
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Finite-Time Stabilization and Impulse Control of Heat Equation with Dynamic Boundary Conditions
In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain....
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On Hyperbolicity Modulo a Closed Subset of Singular Complex Spaces
The purpose of this article is threefold. In 1971, H. L. Royden introduced the Kobayashi-Royden pseudometrics on (nonsingular) complex manifolds and...
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Boundary Smoothness of Holomorphic Map**s
In this chapter we prove, using the scaling method, smooth extension to the boundary of biholomorphic maps between strictly pseudoconvex domains
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On Nonlinear Boundary Value Problems for Differential Inclusions
AbstractWe consider autonomous differential inclusions with nonlinear boundary conditions. Sufficient conditions for the existence of solutions in...
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Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting
A new reformulation of a free boundary problem for the Stokes equations, which govern a viscous flow with an overdetermined condition on the free...
