Results 21 to 30 of about 3,355,987 (326)
Mitigating Transformer Overconfidence via Lipschitz Regularization [PDF]
Conference on Uncertainty in Artificial Intelligence, 2023 Though Transformers have achieved promising results in many computer vision tasks, they tend to be over-confident in predictions, as the standard Dot Product Self-Attention (DPSA) can barely preserve distance for the unbounded input domain. In this work,
Wenqian Ye +3 more
semanticscholar +1 more source
Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics [PDF]
SIAM Journal of Control and Optimization, 2020 We introduce new parametrized classes of shape admissible domains in R n , n ≥ 2, and prove that they are compact with respect to the convergence in the sense of characteristic functions, the Hausdorff sense, the sense of compacts and the weak ...
Michael Hinz +2 more
semanticscholar +1 more source
Smooth approximation of Lipschitz domains, weak curvatures and isocapacitary estimates [PDF]
Calculus of Variations and Partial Differential Equations, 2023 We provide a novel approach to approximate bounded Lipschitz domains via a sequence of smooth, bounded domains. The flexibility of our method allows either inner or outer approximations of Lipschitz domains which also possess weakly defined curvatures ...
Carlo Alberto Antonini
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The Stokes operator in two-dimensional bounded Lipschitz domains [PDF]
Journal of Differential Equations, 2022 . We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain Ω subject to homogeneous Dirichlet boundary conditions. We prove L p -resolvent estimates for p satisfying the condition | 1 /p − 1 / 2 | < 1 / 4 + ε for some ε > 0.
Fabian Gabel, P. Tolksdorf
semanticscholar +1 more source
Lipschitz Regularity of the Eigenfunctions on Optimal Domains [PDF]
Archive for Rational Mechanics and Analysis, 2014 We study the optimal sets $Ω^\ast\subset\mathbb{R}^d$ for spectral functionals $F\big(λ_1(Ω),\dots,λ_p(Ω)\big)$, which are bi-Lipschitz with respect to each of the eigenvalues $λ_1(Ω),\dots,λ_p(Ω)$ of the Dirichlet Laplacian on $Ω$, a prototype being the problem $$ \min{\big\{λ_1(Ω)+\dots+ λ_p(Ω)\;:\;Ω\subset\mathbb{R}^d,\ |Ω|=1\big\}}. $$ We prove the
Bucur, Dorin +3 more
openaire +7 more sources
Existence and multiplicity results for fractional p(x)-Laplacian Dirichlet problem
Moroccan Journal of Pure and Applied Analysis, 2022 In this paper, we study a class of fractional p(x)-Laplacian Dirichlet problems in a bounded domain with Lipschitz boundary. Using variational methods, we prove in different situations the existence and multiplicity of solutions.
Chakrone O. +3 more
doaj +1 more source
Relative Lipschitz-like Property of Parametric Systems via Projectional Coderivatives [PDF]
SIAM Journal on Optimization, 2022 This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property.
Wenfang Yao, Xiaoqi Yang
semanticscholar +1 more source
Riesz transform on exterior Lipschitz domains and applications [PDF]
Advances in Mathematics, 2022 Let ${\mathscr{L}}=-\text{div}A\nabla$ be a uniformly elliptic operator on $\mathbb{R}^n$, $n\ge 2$. Let $\Omega$ be an exterior Lipschitz domain, and let ${\mathscr{L}}_D$ and ${\mathscr{L}}_N$ be the operator ${\mathscr{L}}$ on $\Omega$ subject to the ...
Renjin Jiang, F. Lin
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Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts [PDF]
, 2020 We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition.
Adams, Daniel +4 more
core +4 more sources
On traces for H(curl,Ω) in Lipschitz domains
Journal of Mathematical Analysis and Applications, 2002 AbstractWe study tangential vector fields on the boundary of a bounded Lipschitz domain Ω in R3. Our attention is focused on the definition of suitable Hilbert spaces corresponding to fractional Sobolev regularities and also on the construction of tangential differential operators on the non-smooth manifold.
Annalisa Buffa +2 more
openalex +5 more sources