Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5466
Abstract: Let eℓ, for ℓ = 1,2,3, be orthogonal unit vectors in R3 and let Ω⊂R3 be a bounded open set with smooth boundary ∂Ω. Denoting by x_ a point in Ω, the heat equation, for nonhomogeneous materials,… read more here.
Keywords: fourier law; law; fractional powers; spectrum approach ... See more keywords
Fractional powers of vector operators and fractional Fourier’s law in a Hilbert space
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/aac9e3
Abstract: In this paper we give a concrete application of the spectral theory based on the notion of $S$-spectrum to fractional diffusion process. Precisely, we consider the Fourier law for the propagation of the heat in… read more here.
Keywords: vector; fourier law; law; diffusion ... See more keywords
Hardy inequalities for the fractional powers of the Grushin operator
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DOI: 10.3934/cpaa.2020192
Abstract: We establish uncertainty principles and Hardy inequalities for the fractional Grushin operator, which are reduced to those inequalities for the fractional generalized sublaplacian. The key ingredients to obtain them are an explicit integral representation and… read more here.
Keywords: inequalities fractional; grushin operator; fractional powers; powers grushin ... See more keywords