نتایج جستجو برای: fractional laplacian

تعداد نتایج: 71365  

Journal: :IET Circuits, Devices & Systems 2010
Todd J. Freeborn Brent Maundy Ahmed S. Elwakil

In this study, the authors propose the use of field programmable analogue array hardware to implement an approximated fractional step transfer function of order (n+ a) where n is an integer and 0 , a , 1. The authors show how these filters can be designed using an integer order transfer function approximation of the fractional order Laplacian operator s. First and fourth-order lowand high-pass ...

2011
Juan Luis Vázquez

We describe two models of flow in porous media including nonlocal (longrange) diffusion effects. The first model is based on Darcy’s law and the pressure is related to the density by an inverse fractional Laplacian operator. We prove existence of solutions that propagate with finite speed. The model has the very interesting property that mass preserving self-similar solutions can be found by so...

2009
Ricard Delgado-Gonzalo Pouya Tafti Christophe Rabut Michael Unser

Our aim is to propose a multi-dimensional operator framework that provides a bridge between approximation theory (in particular, the construction of polyharmonic splines and wavelets) and the investigation of self-similar stochastic processes. Our investigation starts with the identification of the linear differential operators that are translation-, scaleand rotation-invariant; these are the f...

2014
D. DE SILVA O. SAVIN

We consider a one-phase free boundary problem involving a fractional Laplacian (−∆), 0 < α < 1, and we prove that “flat free boundaries” are C . We thus extend the known result for the case α = 1/2.

2015
Peter Constantin Mihaela Ignatova MIHAELA IGNATOVA

We prove nonlinear lower bounds and commutator estimates for the Dirichlet fractional Laplacian in bounded domains. The applications include bounds for linear drift-diffusion equations with nonlocal dissipation and global existence of weak solutions of critical surface quasi-geostrophic equations.

Journal: :Asymptotic Analysis 2015
Sunra Mosconi Naoki Shioji Marco Squassina

We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.

Journal: :Calculus of Variations and Partial Differential Equations 2021

In this work we introduce volume constraint problems involving the nonlocal operator $$(-\Delta )_{\delta }^{s}$$ , closely related to fractional Laplacian )^{s}$$ and depending upon a parameter $$\delta >0$$ called horizon. We study associated linear spectral behavior of these when \rightarrow 0^+$$ +\infty $$ . Through limit processes on derive convergence local as respectively, well prove so...

2012
A. CHESKIDOV

We study the incompressible Navier-Stokes equations with a fractional Laplacian and prove the existence of discontinuous LerayHopf solutions in the largest critical space with arbitrarily small initial data.

2015
Jidong Zhao

By meaning of the upper and lower solutions method, we study the existence of positive solutions for a class of q-fractional boundary value problems with p-Laplacian. c ©2015 All rights reserved.

2011
RUPERT L. FRANK

We review our joint result with E. Lenzmann about the uniqueness of ground state solutions of non-linear equations involving the fractional Laplacian and provide an alternate uniqueness proof for an equation related to the intermediate long-wave equation.

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