
Convergence of solutions of discrete semilinear spacetime fractional evolution equations
Let (Δ)_c^s be the realization of the fractional Laplace operator on th...
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Covariant fractional extension of the modified Laplaceoperator used in 3Dshape recovery
Extending the LiouvilleCaputo definition of a fractional derivative to ...
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A series representation of the discrete fractional Laplace operator of arbitrary order
Although fractional powers of nonnegative operators have received much ...
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Simulation of Fractional Brownian Surfaces via Spectral Synthesis on Manifolds
Using the spectral decomposition of the LaplaceBeltrami operator we sim...
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Controllability properties from the exterior under positivity constraints for a 1D fractional heat equation
We study the controllability to trajectories, under positivity constrain...
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Approximation of the spectral fractional powers of the LaplaceBeltrami Operator
We consider numerical approximation of spectral fractional LaplaceBeltr...
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Inversion of trace formulas for a SturmLiouville operator
This paper revisits the classical problem "Can we hear the density of a ...
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Three representations of the fractional pLaplacian: semigroup, extension and Balakrishnan formulas
We introduce three representation formulas for the fractional pLaplace operator in the whole range of parameters 0<s<1 and 1<p<∞. Note that for p 2 this a nonlinear operator. The first representation is based on a splitting procedure that combines a renormalized nonlinearity with the linear heat semigroup. The second adapts the nonlinearity to the CaffarelliSilvestre linear extension technique. The third one is the corresponding nonlinear version of the Balakrishnan formula. We also discuss the correct choice of the constant of the fractional pLaplace operator in order to have continuous dependence as p→ 2 and s → 0^+, 1^. A number of consequences and proposals are derived. Thus, we propose a natural spectraltype operator in domains, different from the standard restriction of the fractional pLaplace operator acting on the whole space. We also propose numerical schemes, a new definition of the fractional pLaplacian on manifolds, as well as alternative characterizations of the W^s,p(ℝ^n) seminorms.
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