Results 1 to 10 of about 393,013 (283)
The trace fractional Laplacian and the mid-range fractional Laplacian [PDF]
Nonlinear Analysis, 2023 In this paper we introduce two new fractional versions of the Laplacian. The first one is based on the classical formula that writes the usual Laplacian as the sum of the eigenvalues of the Hessian. The second one comes from looking at the classical fractional Laplacian as the mean value (in the sphere) of the 1-dimensional fractional Laplacians in ...
Julio D. Rossi, Jorge Ruiz-Cases
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Mellin definition of the fractional Laplacian [PDF]
Fractional Calculus and Applied Analysis, 2023 It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further equivalent definition that is based on the Mellin transform and it can be used when the fractional Laplacian is ...
G. Pagnini, Claudio Runfola
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On the fractional Laplacian of variable order [PDF]
Fractional Calculus and Applied Analysis, 2021 We present a novel definition of variable-order fractional Laplacian on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
Eric F Darve +4 more
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A Class of Fractional p-Laplacian Integrodifferential Equations in Banach Spaces [PDF]
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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The extremal solution for the fractional Laplacian [PDF]
Calculus of Variations and Partial Differential Equations, 2013 We study the extremal solution for the problem $(- )^s u= f(u)$ in $ $, $u\equiv0$ in $\R^n\setminus $, where $ >0$ is a parameter and $s\in(0,1)$. We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded
Xavier Ros‐Oton, Joaquim Serra
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Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian [PDF]
Journal of Function Spaces and Applications, 2013 We study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut ...
Ya-ling Li, Shi-you Lin
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An extension problem for the CR fractional Laplacian [PDF]
Advances in Mathematics, 2014 We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem is different from the one studied, among others, by Caffarelli and Silvestre.
Rupert L. Frank +3 more
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On fractional $p$-Laplacian problems with weight [PDF]
Differential and Integral Equations, 2015 10 ...
Raquel Lehrer +2 more
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The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary [PDF]
, 2013 Xavier Ros‐Oton, Joaquim Serra
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On critical Kirchhoff problems driven by the fractional Laplacian [PDF]
Calculus of Variations and Partial Differential Equations, 2021 We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the Sobolev embedding sense. Our approach is of variational and topological nature.
Luigi Appolloni +2 more
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