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Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4527
Abstract: In this paper, we study the following fractional Schrodinger equations: (−△)αu+λV(x)u=κ|u|q−2u|x|s+β|u|2α∗−2u,u∈Hα(RN),N⩾3,(1) where (−△)α is the fractional Laplacian operator with α∈(0,1),2≤q≤2α,s∗=2(N−s)N−2α≤2α∗=2NN−2α, 0≤s≤2α, λ>0, κ and β are real parameter. 2α∗ is the critical Sobolev exponent. We…
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Keywords:
sobolev;
sobolev exponent;
critical sobolev;
ground state ... See more keywords
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Published in 2018 at "Entropy"
DOI: 10.3390/e20040220
Abstract: We investigate the exponential convergence of a Markovian semigroup in the Zygmund space under the assumption of logarithmic Sobolev inequality. We show that the convergence rate is greater than the logarithmic Sobolev constant. To do…
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Keywords:
space;
sobolev;
convergence markovian;
exponential convergence ... See more keywords
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Published in 2017 at "Canadian Journal of Mathematics"
DOI: 10.4153/cjm-2015-060-3
Abstract: Abstract In this paper, we introduce the anisotropic Sobolev capacity with fractional order and develop some basic properties for this new object. Applications to the theory of anisotropic fractional Sobolev spaces are provided. In particular,…
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Keywords:
anisotropic sobolev;
capacity fractional;
sobolev;
fractional order ... See more keywords