Results 81 to 90 of about 259 (139)

Sobolev Inequalities with Remainder Terms

Journal of Functional Analysis, 1985
Le résultat principal concerne l'inégalité de Sobolev \[ \int_{\Omega}| \nabla u|^ 2\geq S_ n\| u\|^ 2_{2^*}+C(\Omega)[u]^ 2_{2^*/2}. \] Pour toute fonction \(u\in H^ 1_ 0(\Omega)\), où \(\Omega \subset {\mathbb{R}}^ n\) est un ouvert borné, \(S_ n\) est la meilleure constante de Sobolev dans \({\mathbb{R}}^ n\), \(2^*={\mathfrak n}/(n-2)\) et [ \(]_ p\
Brezis, Haïm, Lieb, Elliott H.
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Some inequalities for Sobolev integrals

Electronic Journal of Differential Equations, 2009
We present some inequalities for Sobolev integrals for functions of one variable which are generalization of Dirichlet principle for harmonic functions.
Stepan Tersian, Nikolaj Dimitrov
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Hardy–Sobolev interpolation inequalities

Calculus of Variations and Partial Differential Equations
AbstractWe derive a family of interpolation estimates which improve Hardy’s inequality and cover the Sobolev critical exponent. We also determine all optimizers among radial functions in the endpoint case and discuss open questions on nonrestricted optimizers.
Charlotte Dietze, Phan Thành Nam
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q− Fractional Inequalities

Cubo, 2011
Here we give q−fractional Poincaré type, Sobolev type and Hilbert-Pachpatte type integral inequalities, involving q−fractional derivatives of functions.
George A Anastassiou
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Hardy and Sobolev inequalities on antisymmetric functions

Bulletin of Mathematical Sciences
We obtain sharp Hardy inequalities on antisymmetric functions, where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the paper [Th. Hoffmann-Ostenhof and A.
Th. Hoffmann-Ostenhof, A. Laptev, I. Shcherbakov   +2 more
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On weighted Calderón-Zygmund singular integrals and applications

Journal of Innovative Applied Mathematics and Computational Sciences, 2022
This paper studies some weighted norm inequalities related to some Calderon-Zygmund singular integrals. Applications to the Sobolev-Gagliardo-Nirenberg inequality, differential forms, and the potential equation du = f are given.
Ahmed Loulit
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Nonlinear Elliptic Equations with Maximal Growth Range

Pesquimat, 2017
In this work we are interested in studying the existence of nontrivial weak solutions for a class of nonlinear elliptic equations defined in a bounded domain in dimension two, where the nonlinearities possess maximal exponential growth range motivated by
Yony Raúl Santaria Leuyacc
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Poincaré and Log–Sobolev Inequalities for Mixtures [PDF]

Entropy, 2019
This work studies mixtures of probability measures on R n and gives bounds on the Poincaré and the log–Sobolev constants of two-component mixtures provided that each component satisfies the functional inequality, and both components are close in the χ 2 -distance.
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Hardy-Littlewood-Sobolev Inequalities on p-Adic Central Morrey Spaces

Journal of Function Spaces, 2015
We establish the Hardy-Littlewood-Sobolev inequalities on p-adic central Morrey spaces. Furthermore, we obtain the λ-central BMO estimates for commutators of p-adic Riesz potential on p-adic central Morrey spaces.
Qing Yan Wu, Zun Wei Fu
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Stability for the Sobolev inequality in cones

Journal of Differential Equations
We prove a quantitative Sobolev inequality in cones of Bianchi-Egnell type, which implies a stability property. Our result holds for any cone as long as the minimizers of the Sobolev quotient are nondegenerate, which is the case of most cones. When the minimizers are the classical bubbles we have more precise results.
Giulio Ciraolo, Filomena Pacella, Camilla Chiara Polvara   +2 more
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