Results 1 to 10 of about 259 (139)
Sobolev-Kantorovich Inequalities
Analysis and Geometry in Metric Spaces, 2015 In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich ...
Ledoux Michel
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Fractional Gagliardo–Nirenberg interpolation inequality and bounded mean oscillation
Comptes Rendus. Mathématique, 2023 We prove Gagliardo–Nirenberg interpolation inequalities estimating the Sobolev semi-norm in terms of the bounded mean oscillation semi-norm and of a Sobolev semi-norm, with some of the Sobolev semi-norms having fractional order.
Van Schaftingen, Jean
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SOBOLEV INEQUALITIES WITH SYMMETRY [PDF]
Communications in Contemporary Mathematics, 2009 In this paper, we derive some Sobolev inequalities for radially symmetric functions in Ḣswith 1/2 < s < n/2. We show the end point case s = 1/2 on the homogeneous Besov space [Formula: see text]. These results are extensions of the well-known Strauss' inequality [13].
Cho, Yonggeun, Ozawa, Tohru
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A modified Φ-Sobolev inequality for canonical Lévy processes and its applications
Modern Stochastics: Theory and Applications, 2023 A new modified Φ-Sobolev inequality for canonical ${L^{2}}$-Lévy processes, which are hybrid cases of the Brownian motion and pure jump-Lévy processes, is developed.
Noriyoshi Sakuma, Ryoichi Suzuki
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Lupaş-type inequality and applications to Markov-type inequalities in weighted Sobolev spaces
Bulletin of Mathematical Sciences, 2021 Weighted Sobolev spaces play a main role in the study of Sobolev orthogonal polynomials. In particular, analytic properties of such polynomials have been extensively studied, mainly focused on their asymptotic behavior and the location of their zeros. On
Francisco Marcellán +1 more
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Logarithmic estimates for mean-field models in dimension two and the Schrödinger–Poisson system
Comptes Rendus. Mathématique, 2022 In dimension two, we investigate a free energy and the ground state energy of the Schrödinger–Poisson system coupled with a logarithmic nonlinearity in terms of underlying functional inequalities which take into account the scaling invariances of the ...
Dolbeault, Jean +2 more
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Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications
Open Mathematics, 2023 Let m∈Nm\in {\mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces Wm,φ(Rn){W}^{m,\varphi }\left({{\mathbb{R}}}^{n}).
Wu Ruimin, Wang Songbai
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Degenerate Poincaré–Sobolev inequalities [PDF]
Transactions of the American Mathematical Society, 2019 We study weighted Poincaré and Poincaré-Sobolev type inequalities with an explicit analysis on the dependence on the $A_p$ constants of the involved weights. We obtain inequalities of the form $$ \left (\frac{1}{w(Q)}\int_Q|f-f_Q|^{q}w\right )^\frac{1}{q}\le C_w\ell(Q)\left (\frac{1}{w(Q)}\int_Q |\nabla f|^p w\right )^\frac{1}{p}, $$ with different ...
Pérez, C., Rela, E.
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Weighted Norm Inequalities for Multilinear Fourier Multipliers with Mixed Norm
Abstract and Applied Analysis, 2021 In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the Lr-based Sobolev ...
Mai Fujita
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The Caffarelli–Kohn–Nirenberg inequalities for radial functions
Comptes Rendus. Mathématique, 2023 We establish the full range of the Caffarelli–Kohn–Nirenberg inequalities for radial functions in the Sobolev and the fractional Sobolev spaces of order $0 < s \le 1$.
Mallick, Arka, Nguyen, Hoai-Minh
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