Sharp Hardy—Leray inequality for axisymmetric divergence-free fields

Costin, O.; Maz'ya, V.
August 2008
Calculus of Variations & Partial Differential Equations;Aug2008, Vol. 32 Issue 4, p523
Academic Journal
We show that the sharp constant in the classical n-dimensional Hardy–Leray inequality can be improved for axisymmetric divergence-free fields, and find its optimal value. The same result is obtained for n = 2 without the axisymmetry assumption.


Related Articles

  • Existence of Continuous Functions with a Given Order of Decrease of Least Deviations from Rational Approximations. Starovoitov, A. P. // Mathematical Notes;Nov/Dec2003, Vol. 74 Issue 5/6, p701 

    For a given strictly decreasing sequence \ a_n\^\infty_{n=0} of real numbers convergent to zero, we construct a continuous function g on the closed interval [-1,1] such that R_{2n}(g) and a_n have identical order of decrease as...

  • THE SET OF CONTINUOUS PIECEWISE DIFFERENTIABLE FUNCTIONS. Sofronidis, Nikolaus Efstathiou // Real Analysis Exchange;2005/2006, Vol. 31 Issue 1, p13 

    The purpose of this article is to show that if - ∞ < α < β < ∞, then the set PDαβ of piecewise differentiable functions in C([α, β],ℝ) is π1¹-complete.

  • On Lie ideals with generalized derivations. Gölbaşı, Ö.; Kaya, K. // Siberian Mathematical Journal;Sep2006, Vol. 47 Issue 5, p862 

    Let R be a prime ring with characteristic different from 2, let U be a nonzero Lie ideal of R, and let f be a generalized derivation associated with d. We prove the following results: (i) If a ∊ R and [a, f(U)] = 0 then a ∊ Z or d(a) = 0 or U ⊂ Z; (ii) If f²(U) = 0 then U...

  • Faber Polynomial Coefficients of Classes of Meromorphic Bistarlike Functions. Jahangiri, Jay M.; Hamidi, Samaneh G. // International Journal of Mathematics & Mathematical Sciences;10/4/2015, Vol. 2015, p1 

    Applying the Faber polynomial coefficient expansions to certain classes of meromorphic bistarlike functions, we demonstrate the unpredictability of their early coefficients and also obtain general coefficient estimates for such functions subject to a given gap series condition. Our results...

  • ADDITIVE PROPERTIES OF CERTAIN CLASSES OF PATHOLOGICAL FUNCTIONS. Kharazishvili, Alexander B.; Razmadze, A. // Real Analysis Exchange;2013, Vol. 38 Issue 2, p475 

    Some additive properties of the following three families of "pathological" functions are briefly discussed: continuous nowhere differentiable functions, Sierpiński-Zygmund functions, and absolutely nonmeasurable functions. INSET: '.

  • ALGEBRAIC SUMS OF SETS IN MARCZEWSKI-BURSTIN ALGEBRAS. Dorais, François G.; Filipów, Rafal // Real Analysis Exchange;2005/2006, Vol. 31 Issue 1, p133 

    Using almost-invariant sets, we show that a family of Marczewski-Burstin algebras over groups are not closed under algebraic sums. We also give an application of almost-invariant sets to the difference property in the sense of de Bruijn. In particular, we show that if G is a perfect Abelian...

  • Distribution of the best nonzero differential and linear approximations of s-box functions. Chmiel, Krzysztof // Journal of Telecommunications & Information Technology;2006, Vol. 2006 Issue 3, p8 

    In the paper the differential and the linear approximations of two classes of s-box functions are considered. The classes are the permutations and arbitrary functions with n binary inputs and m binary outputs, where 1 ≤ n = m ≤ 10. For randomly chosen functions from each of the...

  • The Structure Function and Distinguishable Models of Data. Rissanen, J. // Computer Journal;Nov2006, Vol. 49 Issue 6, p657 

    The article provides information on various useful complex models and their respective structure functions to be used in various mathematical models. It highlights various structure functions for mathematical operations and notes their different models including mixture model and normalized...

  • FINITE-DEGREE UTILITY INDEPENDENCE. Fishburn, Peter C.; Farquhar, Peter H. // Mathematics of Operations Research;Aug82, Vol. 7 Issue 3, p348 

    When u is a von Neumann-Morgenstern utility function on X ⊗ Y. Y is ‘utility independent’ of X if u can be written as u(x, y)=f(x)g(y) + a(x) with f positive. This paper introduces a fundamental extension of utility independence that is base on induced indifference relations...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics