Articles with "sobolev" as a keyword



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Ground state of solutions for a class of fractional Schrödinger equations with critical Sobolev exponent and steep potential well

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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… read more here.

Keywords: sobolev; sobolev exponent; critical sobolev; ground state ... See more keywords
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Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space

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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… read more here.

Keywords: space; sobolev; convergence markovian; exponential convergence ... See more keywords
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Anisotropic Sobolev Capacity with Fractional Order

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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,… read more here.

Keywords: anisotropic sobolev; capacity fractional; sobolev; fractional order ... See more keywords