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
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
Lipschitz stability for determination of states and inverse source problem for the mean field game equations [PDF]
Inverse Problems and Imaging, 2023 In a bounded domain $\Omega \subset \mathbb{R}^d$ over time interval $(0,T)$, we consider mean field game equations whose principal coefficients depend on the time and state variables with a general Hamiltonian.
O. Imanuvilov, Hongyu Liu, M. Yamamoto
semanticscholar +1 more source
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
doaj +1 more source
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 the traces of w2,p() for a lipschitz domain
, 2001 Ricardo G. Durán +1 more
openalex +3 more sources
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
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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Asymptotic Stability for the 2D Navier–Stokes Equations with Multidelays on Lipschitz Domain
Mathematics, 2022 This paper is concerned with the asymptotic stability derived for the two-dimensional incompressible Navier–Stokes equations with multidelays on Lipschitz domain, which models the control theory of 2D fluid flow. By a new retarded Gronwall inequality and
Ling-Rui Zhang +2 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
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