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Interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces
interpolation inequality Landau-Kolmogorov type inequality Variable exponent Lebesgue-Sobolev space maximal function operator
2011/10/26
The author shows the interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces by applying the boundedness of the Hardy-Littlewood maximal operator on L^{p(x)}. As applic...
Algebra properties for Sobolev spaces- Applications to semilinear PDE's on manifolds
Sobolev spaces Riemannian manifold algebra rule paraproducts heat semigroup
2011/9/15
Abstract: In this work, we aim to prove algebra properties for generalized Sobolev spaces $W^{s,p} \cap L^\infty$ on a Riemannian manifold, where $W^{s,p}$ is of Bessel-type $W^{s,p}:=(1+L)^{-s/m}(L^p...
Global solutions for the generalized Boussinesq equation in low-order Sobolev spaces
Global solutions generalized Boussinesq equation low-order Sobolev spaces
2010/12/14
We show that the Cauchy problem for the defocusing generalized Boussinesq equation utt − uxx + uxxxx − (|u|2ku)xx = 0, k 1, on the real line is globally well-posed in Hs(R) for s > 1W...