Results 161 to 170 of about 71,930 (202)
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Canadian Mathematical Bulletin, 1988
AbstractThe Sobolev inequality of ordermasserts that ifp≧ 1,mp<nand1/q = 1/p — m/n,then the Lq-norm of a smooth function with compact support in Rnis bounded by a constant times the sum of theLp-norms of the partial derivatives of ordermof that function.
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AbstractThe Sobolev inequality of ordermasserts that ifp≧ 1,mp<nand1/q = 1/p — m/n,then the Lq-norm of a smooth function with compact support in Rnis bounded by a constant times the sum of theLp-norms of the partial derivatives of ordermof that function.
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A Sobolev Interpolation Inequality and a Gross-Sobolev Logarithmic Inequality
Mathematical Notes, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Degenerate Sobolev inequalities from the classical Sobolev inequality
Analysis and Mathematical PhysicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
ZEREN, Yusuf +3 more
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HEISENBERG'S INEQUALITY IN SOBOLEV SPACES
Acta Mathematica Scientia, 2000The inequality that is known as Heisenberg's uncertainty principle is extended to Sobolev spaces by using Weyl symbols, pseudodifferential operators and parametrized Fourier transforms. The result is supposed to be applicable to those problems in quantum mechanics which cannot be adequately modelled by the Hilbert space formalism.
Qi, Minyou, Tian, Guji
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Applicable Analysis, 2007
We present two-scale Morrey–Sobolev inequalities for measure-valued Lagrangeans on quasi-metric balls, scaled according to refined power laws. The fine tuning is given by suitable gauge functions, typically of logarithmic type. Fractal examples with fluctuating geometry are described.
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We present two-scale Morrey–Sobolev inequalities for measure-valued Lagrangeans on quasi-metric balls, scaled according to refined power laws. The fine tuning is given by suitable gauge functions, typically of logarithmic type. Fractal examples with fluctuating geometry are described.
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Sharp convex Lorentz–Sobolev inequalities
Mathematische Annalen, 2010The Lorentz-Sobolev inequality has a long history. The geometric analogue of the \(L^1\)-Sobolev inequality is the Euclidean isoperimetric inequality. New sharp Lorentz-Sobolev inequalities are obtained by convexifying level sets in Lorentz integrals via the \(L^p\)-Minkowski problem.
Ludwig, Monika +2 more
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Logarithmic Sobolev Inequalities
2014After Poincare inequalities, logarithmic Sobolev inequalities are amongst the most studied functional inequalities for semigroups. They contain much more information than Poincare inequalities, and are at the same time sufficiently general to be available in numerous cases of interest, in particular in infinite dimension (as limits of Sobolev ...
Dominique Bakry +2 more
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Sobolev inequalities on homogeneous spaces
Potential Analysis, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BIROLI, MARCO, MOSCO U.
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1991
A weak Sobolev inequality (WSI) is a weakened form of a Sobolev inequality associated to a Dirichlet form. It turns out that it is in fact equivalent to a Sobolev inequality. If there is a spectral gap and a (WSI) holds, then we can get a tight weake Sobolev quality (TWSI). Starting with a TWSI.
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A weak Sobolev inequality (WSI) is a weakened form of a Sobolev inequality associated to a Dirichlet form. It turns out that it is in fact equivalent to a Sobolev inequality. If there is a spectral gap and a (WSI) holds, then we can get a tight weake Sobolev quality (TWSI). Starting with a TWSI.
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Logarithmic Sobolev Inequalities
1984There is an interesting connection between our considerations here and L. Gross’s theory of logarithmic Sobolev inequalities. For our purposes, it is best to describe a logarithmic Sobolev inequality in the following terms. Let {Px: x ∈ E} satisfy (S.C.) with respect to m ∈ m1 (E).
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