Results 31 to 40 of about 5,262 (196)
Communications in Partial Differential Equations, 2014 We compare two natural types of fractional Laplacians $(-Δ)^s$, "Navier" and "Dirichlet" ones.
MUSINA, Roberta, Nazarov A. I.
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Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]
, 2009 Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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A detour on a class of nonlocal degenerate operators
Bruno Pini Mathematical Analysis Seminar, 2023 We present some recent results on a class of degenerate operators which are modeled on the fractional Laplacian, converge to the truncated Laplacian, and are extremal among operators with fractional diffusion along subspaces of possibly different ...
Delia Schiera
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On the fractional p-Laplacian problems [PDF]
Journal of Inequalities and Applications, 2021 AbstractThis paper deals with nonlocal fractionalp-Laplacian problems with difference. We get a theorem which shows existence of a sequence of weak solutions for a family of nonlocal fractionalp-Laplacian problems with difference. We first show that there exists a sequence of weak solutions for these problems on the finite-dimensional subspace. We next
Q-Heung Choi, Tacksun Jung
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Generic properties of eigenvalues of the fractional Laplacian [PDF]
, 2023 We consider the Dirichlet eigenvalues of the fractional Laplacian, related to a smooth bounded domain. We prove that there exists an arbitrarily small perturbation of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian are
Micheletti A. M. +3 more
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On fractional Laplacians $– 2$
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2016 For s > −1 we compare two natural types of fractional Laplacians (−\mathrm{\Delta })^{s} , namely, the “Navier” and the “Dirichlet” ones.
Roberta Musina, Alexander I. Nazarov
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Local Energy Estimates for the Fractional Laplacian [PDF]
SIAM Journal on Numerical Analysis, 2021 The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the ...
Juan Pablo Borthagaray +2 more
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Nonnegative solutions of nonlinear fractional Laplacian equations [PDF]
, 2020 The study of reaction-diffusion equations involving nonlocal diffusion operators has recently flourished. The fractional Laplacian is an example of a nonlocal diffusion operator which allows long-range interactions in space, and it is therefore important
Hollifield, Elliott Z. +1 more
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Path Laplacians versus fractional Laplacians as nonlocal operators on networks
New Journal of Physics, 2021 Here we study and compare nonlocal diffusion processes on networks based on two different kinds of Laplacian operators. We prove that a nonlocal diffusion process on a network based on the path Laplacian operator always converges faster than the standard
Ernesto Estrada
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On the existence of ground state solutions to critical growth problems nonresonant at zero
Comptes Rendus. Mathématique, 2021 We prove the existence of ground state solutions to critical growth $p$-Laplacian and fractional $p$-Laplacian problems that are nonresonant at zero.
Perera, Kanishka
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