Integral inequalities of Wirtinger-type and fourth-order elliptic differential inequalities
نویسندگان
چکیده
منابع مشابه
Lyapunov-type integral inequalities for certain higher order differential equations
In this paper, we obtain Liapunov-type integral inequalities for certain nonlinear, nonhomogeneous differential equations of higher order with without any restriction on the zeros of their higher-order derivatives of the solutions by using elementary analysis. As an applications of our results, we show that oscillatory solutions of the equation converge to zero as t → ∞. Using these inequalitie...
متن کاملOn Pinsker's Type Inequalities and Csiszar's f-divergences. Part I: Second and Fourth-Order Inequalities
We study conditions on f under which an f -divergence Df will satisfy Df ≥ cfV 2 or Df ≥ c2,fV 2 + c4,fV 4, where V denotes variational distance and the coefficients cf , c2,f and c4,f are best possible. As a consequence, we obtain lower bounds in terms of V for many well known distance and divergence measures. For instance, let D(α)(P,Q) = [α(α−1)]−1[∫ qαp1−α dμ−1] and Iα(P,Q) = (α−1)−1 log[ ∫...
متن کاملHardy Type Inequalities Related to Degenerate Elliptic Differential Operators
We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators Lpu := −∇ ∗ L(|∇Lu| ∇Lu). If φ is a positive weight such that −Lpφ ≥ 0, then the Hardy type inequality c ∫ Ω |u| φp |∇Lφ| p dξ ≤ ∫
متن کاملHardy Type Inequalities for Integral Transforms Associated with a Singular Second Order Differential Operator
We consider a singular second order differential operator ∆ defined on ]0,∞[. We give nice estimates for the kernel which intervenes in the integral transform of the eigenfunction of ∆. Using these results, we establish Hardy type inequalities for Riemann-Liouville and Weyl transforms associated with the operator ∆.
متن کاملWirtinger Inequalities , Cayley 4 - Form , and Homotopy
We study optimal curvature-free inequalities of the type discovered by C. Loewner and M. Gromov, using a generalisation of the Wirtinger inequality for the comass. Using a model for the classifying space BS built inductively out of BS, we prove that the symmetric metrics of certain two-point homogeneous manifolds turn out not to be the systolically optimal metrics on those manifolds. We point o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1972
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1972.40.739