Results 21 to 30 of about 3,089 (88)
Sobolev inequalities for the Hardy-Schr\"odinger operator: Extremals and critical dimensions [PDF]
, 2015 In this expository paper, we consider the Hardy-Schr\"odinger operator $-\Delta -\gamma/|x|^2$ on a smooth domain \Omega of R^n with 0\in\bar{\Omega}, and describe how the location of the singularity 0, be it in the interior of \Omega or on its boundary,
Ghoussoub, Nassif, Robert, Frédéric
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Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations [PDF]
, 2012 The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form $-\Delta u= c u^p$, with ...
Bonforte, Matteo +2 more
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Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations [PDF]
, 2015 We prove that local and global parabolic BMO spaces are equal thus extending the classical result of Reimann and Rychener. Moreover, we show that functions in parabolic BMO are exponentially integrable in a general class of space-time cylinders.
Saari, Olli
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On the Stability of Solitary Water Waves with a Point Vortex
Communications on Pure and Applied Mathematics, Volume 73, Issue 12, Page 2634-2684, December 2020., 2020 This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small‐amplitude waves with small enough vortex strength are conditionally orbitally stable. In the process of obtaining this result, we develop a quite general stability/instability theory for ...
Kristoffer Varholm +2 more
wiley +1 more source
An extension of the classical John-Nirenberg inequality of martingales
AIMS Mathematics, 2022 <abstract><p>In this paper, we prove the John-Nirenberg theorem of the $ bmo_p $ martingale spaces for the full range $ 0 < p < \infty $. We also consider the John-Nirenberg inequality on symmetric spaces of martingales.</p></abstract>
Changzheng Yao, Congbian Ma
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Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 In this paper, we first introduce some new classes of weighted amalgam spaces. Then, we give the weighted strong‐type and weak‐type estimates for fractional integral operators Iγ on these new function spaces. Furthermore, the weighted strong‐type estimate and endpoint estimate of linear commutators [b, Iγ] generated by b and Iγ are established as well.
Hua Wang, Kehe Zhu
wiley +1 more source
Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential [PDF]
, 2004 We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear ...
Carles R. +13 more
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Uchiyama's lemma and the John-Nirenberg inequality [PDF]
Bulletin of the London Mathematical Society, 2013 Using integral formulas based on Green's theorem and in particular a lemma of Uchiyama, we give simple proofs of comparisons of different BMO norms without using the John-Nirenberg inequality while we also give a simple proof of the strong John-Nirenberg inequality. Along the way we prove the inclusions of BMOA in the dual of H^1 and BMO in the dual of
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The John–Nirenberg inequality for Orlicz–Lorentz spaces in a probabilistic setting
Revista de la Unión Matemática Argentina, 2023 Summary: The John-Nirenberg inequality is widely studied in the field of mathematical analysis and probability theory. In this paper we study a new type of the John-Nirenberg inequality for Orlicz-Lorentz spaces in a probabilistic setting. To be precise, let \(0 < q \leq \infty\) and \(\Phi\) be an \(N\)-function with some proper restrictions. We prove
Li, Libo, Hao, Zhiwei
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Abstract and Applied Analysis, Volume 2020, Issue 1, 2020., 2020 Let 0 < γ < n and Iγ be the fractional integral operator of order γ, Iγfx=∫ℝnx−yγ−nfydy and let [b, Iγ] be the linear commutator generated by a symbol function b and Iγ, [b, Iγ]f(x) = b(x) · Iγf(x) − Iγ(bf)(x). This paper is concerned with two‐weight, weak‐type norm estimates for such operators on the weighted Morrey and amalgam spaces.
Hua Wang, Paul W. Eloe
wiley +1 more source