Results 31 to 40 of about 3,355,987 (326)
On the traces of w2,p() for a lipschitz domain
, 2001 Ricardo G. Durán +1 more
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Uniform Convergence Rates for Lipschitz Learning on Graphs [PDF]
arXiv.org, 2021 Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph.
Leon Bungert, J. Calder, Tim Roith
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LipBaB: Computing exact Lipschitz constant of ReLU networks [PDF]
International Conference on Artificial Neural Networks, 2021 The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers.
Aritra Bhowmick +2 more
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On functions subharmonic in a Lipschitz domain [PDF]
Proceedings of the American Mathematical Society, 1978 Let D be a starlike Lipschitz domain in R n , n ⩾ 2 {R^n},n \geqslant 2 . If w is a subharmonic function in D with positive harmonic majorant, then at almost every point on the boundary of D (surface measure), w has radial limit.
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The Martin boundary in non-Lipschitz domains [PDF]
Transactions of the American Mathematical Society, 1993 The Martin boundary with respect to the Laplacian \(\Delta\) and with respect to a uniformly elliptic operator \(L\) in divergence form is considered for a wider class than the Lipschitz domains in \(\mathbb{R}^ d\), \(d \geq 3\). For a so-called bounded \(C^ \gamma\) domain \(D\) it is shown that the Martin boundary of \(D\) and its Euclidean boundary
Burdzy, Krzysztof, Bass, Richard F.
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An inverse problem for a hyperbolic system in a bounded domain
Comptes Rendus. Mathématique, 2023 In this Note we consider a two-by-two hyperbolic system defined on a bounded domain. Using Carleman inequalities, we obtain a Lipschitz stability result for the four spatially varying coefficients with measurements of only one component, given two sets ...
Cardoulis, Laure
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Boundary value problems on non-Lipschitz uniform domains: stability, compactness and the existence of optimal shapes [PDF]
Asymptotic Analysis, 2021 We study boundary value problems for bounded uniform domains in R n , n ⩾ 2 , with non-Lipschitz, and possibly fractal, boundaries. We prove Poincaré inequalities with uniform constants and trace terms for ( ε , ∞ ) -domains contained in a fixed bounded ...
Michael Hinz +2 more
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Boundary Integral Operator for the Fractional Laplace Equation in a Bounded Lipschitz Domain [PDF]
, 2011 We study the boundary integral operator induced from fractional Laplace equation in a bounded Lipschitz domain. As an application, we study the boundary value problem of a fractional Laplace equation.
Tongkeun Chang
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Extending the Applicability of Two-Step Solvers for Solving Equations
Mathematics, 2019 We present a local convergence of two-step solvers for solving nonlinear operator equations under the generalized Lipschitz conditions for the first- and second-order derivatives and for the first order divided differences.
Ioannis K. Argyros, Stepan Shakhno
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Variational formulas on Lipschitz domains [PDF]
Transactions of the American Mathematical Society, 1995 A rigorous treatment is given of variational formulas for solutions of certain Dirichlet problems for the Laplace operator on Lipschitz domains under interior variations. In particular we extend well-known variational formulas for the torsional rigidity and for capacity from the class of C 1 {C^1 ...
Elcrat, Alan R., Miller, Kenneth G.
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