A mixed operator approach to peridynamics
Mathematics in Engineering, 2023 In the present paper we propose a model describing the nonlocal behavior of an elastic body using a peridynamical approach. Indeed, peridynamics is a suitable framework for problems where discontinuities appear naturally, such as fractures, dislocations,
Federico Cluni +4 more
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Overdetermined problems with fractional laplacian [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2015 Added a missing assumption (1.3) in Theorem 1.1 and Theorem 1.2, which is used in the proof of Lemma 4 ...
Fall, Mouhamed Moustapha, Jarohs, Sven
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Existence of Multiple Weak Solutions to a Discrete Fractional Boundary Value Problem
Axioms, 2023 The existence of at least three weak solutions to a discrete fractional boundary value problem containing a p-Laplacian operator and subject to perturbations is proved using variational methods. Some applications of the main results are presented.
Shahin Moradi +2 more
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Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules [PDF]
, 2015 It has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties as a fractional Laplacian. This has led to the hope that the homogenous Boltzmann equation enjoys similar regularity properties as the heat equation with ...
Barbaroux, Jean-Marie +3 more
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Getting Acquainted with the Fractional Laplacian [PDF]
, 2019 updated version, 72 pages, 12 ...
Abatangelo N., Valdinoci E.
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A Class of Fractional p-Laplacian Integrodifferential Equations in Banach Spaces
Abstract and Applied Analysis, 2013 We study a class of nonlinear fractional integrodifferential equations with p-Laplacian operator in Banach space. Some new existence results are obtained via fixed point theorems for nonlocal boundary value problems of fractional p-Laplacian equations ...
Yiliang Liu, Liang Lu
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Solutions for the Problems Involving Fractional Laplacian and Indefinite Potentials
Advanced Nonlinear Studies, 2017 In this paper, we consider a class of Schrödinger equations involving fractional Laplacian and indefinite potentials. By modifying the definition of the Nehari–Pankov manifold, we prove the existence and asymptotic behavior of least energy solutions.
Tang Zhongwei, Wang Lushun
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Point-like perturbed fractional Laplacians through shrinking potentials of finite range
, 2018 We reconstruct the rank-one, singular (point-like) perturbations of the $d$-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schr\"{o}dinger operators with regular potentials centred around the perturbation
Michelangeli, Alessandro +1 more
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Principal eigenvalue of the fractional Laplacian with a large incompressible drift [PDF]
, 2013 We add a divergence-free drift with increasing magnitude to the fractional Laplacian on a bounded smooth domain, and discuss the behavior of the principal eigenvalue for the Dirichlet problem.
Bogdan, Krzysztof, Komorowski, Tomasz
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On the Laplacian and fractional Laplacian in an exterior domain
Advances in Differential Equations, 2012 We see that the generalized Fourier transform due to A.G. Ramm for the case of $n=3$ space dimensions remains valid, with some modifications, for all space dimensions $n\ge 2$. We use the resulting spectral representation of the exterior Laplacian to study exterior problems. In particular the Fourier splitting method developed by M.E.
Kosloff, Leonardo, Schonbek, Tomas
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