Related papers: Some inequalities for complete elliptic integrals
We prove Harnack's inequality for bounded weak solutions to quasilinear second order elliptic equations with generalized Orlicz growth conditions. Our approach covers new cases of variable exponent and (p,q) growth conditions.
We review some results about quantitative improvements of sharp inequalities for eigenvalues of the Laplacian.
We present an elliptic version of Selberg's integral formula.
The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed…
The estimate in Bullen's inequality will be extended for continuous functions using the second order modulus of smoothness. A different form of this inequality will be given in terms of the least concave majorant. Also, the composite case…
We consider some integral-geometric quantities that have recently arisen in harmonic analysis and elsewhere, derive some sharp geometric inequalities relating them, and place them in a wider context.
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct inequalities of special means.
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
In this paper, the author obtains new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive reals…
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
A new variational approach to solve the problem of estimating the (possibly discontinuous) coefficient functions $p$, $q$ and $f$ in elliptic equations of the form $-\nabla \cdot (p(x)\nabla u) + \lambda q(x) u = f$, $x \in \Omega \subset…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
We extend an inequality for harmonic functions, obtained in previous research by the authors, to the case of solutions of uniformly elliptic equations in divergence form, with merely measurable coefficients. The inequality for harmonic…
Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.
We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order…
Solutions to elliptic equations often exhibit higher regularity properties such as \emph{higher integrability}. That is, for instance, a solution $u$ to a system that a priori only satisfies $ u \in W^{1,r}$ is more regular and even in the…
In this paper, we establish new an inequality of weighted Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…