Inequalities in the A-Harmonic Equations and the Related Topics
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Citation: Journal of Inequalities and Applications 2010 2010:809380
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-Weighted Inequalities with Lipschitz and BMO Norms
We first define a new kind of two-weight, then obtain some two-weight integral inequalities with Lipschitz norm and BMO norm for Green'...
Citation: Journal of Inequalities and Applications 2010 2010:589040 -
Periodic Systems Dependent on Parameters
This paper is concerned with a periodic system dependent on parameter. We study differentiability with respect to parameters of the periodic solution of the system. Applying a fixed point theorem and the resul...
Citation: Journal of Inequalities and Applications 2010 2010:796165 -
Orlicz Sequence Spaces with a Unique Spreading Model
We study the set of all spreading models generated by weakly null sequences in Orlicz sequence spaces equipped with partial order by domination. A sufficient and necessary condition for the above-mentioned set...
Citation: Journal of Inequalities and Applications 2010 2010:962842 -
Gradient Estimates for Weak Solutions of -Harmonic Equations
We obtain gradient estimates in Orlicz spaces for weak solutions of -Harmonic Equations under the assumptions that ...
Citation: Journal of Inequalities and Applications 2010 2010:685046 -
Decomposition of Polyharmonic Functions with Respect to the Complex Dunkl Laplacian
Let be a -invariant convex domain in ...
Citation: Journal of Inequalities and Applications 2010 2010:947518 -
Existence of Solutions of Second Order Boundary Value Problems with Integral Boundary Conditions and Singularities
By the notation and monotone convergence theorem of Henstock-Kurzweil integral, we investigate the existence of continuous solutions for the second order boundary value problems with integral boundary conditio...
Citation: Journal of Inequalities and Applications 2010 2010:807178 -
On Harmonic Quasiconformal Quasi-Isometries
The purpose of this paper is to explore conditions which guarantee Lipschitz-continuity of harmonic maps with respect to quasihyperbolic metrics. For instance, we prove that harmonic quasiconformal maps are Li...
Citation: Journal of Inequalities and Applications 2010 2010:178732 -
Uniform Convergence of Some Extremal Polynomials in Domain with Corners on the Boundary
The aim of this paper is to investigate approximation properties of some extremal polynomials in , ...
Citation: Journal of Inequalities and Applications 2010 2010:716176 -
Some Priori Estimates about Solutions to Nonhomogeneous A-Harmonic Equations
We deal with the nonhomogeneous A-harmonic equation and the related conjugate A-harmonic equation ...
Citation: Journal of Inequalities and Applications 2010 2010:520240 -
Weighted Decomposition Estimates for Differential Forms
After introducing the definition of -weights, we establish the
Citation: Journal of Inequalities and Applications 2010 2010:649340 -
A-Harmonic Equations and the Dirac Operator
We show how -harmonic equations arise as components of Dirac systems. We generalize ...
Citation: Journal of Inequalities and Applications 2010 2010:124018 -
The Obstacle Problem for the -Harmonic Equation
Firstly, we define an order for differential forms. Secondly, we also define the supersolution and subsolution of the -harmonic equation and the...
Citation: Journal of Inequalities and Applications 2010 2010:767150 -
First-Order Twistor Lifts
The use of twistor methods in the study of Jacobi fields has proved quite fruitful, leading to a series of results. L. Lemaire and J. C. Wood proved several properties of Jacobi fields along harmonic maps from...
Citation: Journal of Inequalities and Applications 2010 2010:594843 -
Global Estimates for Singular Integrals of the Composition of the Maximal Operator and the Green's Operator
We establish the Poincaré type inequalities for the composition of the maximal operator and the Green's operator in John domains.
Citation: Journal of Inequalities and Applications 2010 2010:723234 -
Optimal Interior Partial Regularity for Nonlinear Elliptic Systems for the Case under Natural Growth Condition
We consider the interior regularity for weak solutions of second-order nonlinear elliptic systems with subquadratic growth under natural growth condition. We obtain a general criterion for a weak solution to b...
Citation: Journal of Inequalities and Applications 2010 2010:680714 -
Some Estimates of Integrals with a Composition Operator
We give some estimates of integrals with a composition operator, namely, composition of homotopy, differential, and Green's operators , ...
Citation: Journal of Inequalities and Applications 2010 2010:928150 -
Global Existence and Asymptotic Behavior of Solutions for Some Nonlinear Hyperbolic Equation
The initial boundary value problem for a class of hyperbolic equation with nonlinear dissipative term in a bounded domain is studied. T...
Citation: Journal of Inequalities and Applications 2010 2010:895121 -
Local Regularity and Local Boundedness Results for Very Weak Solutions of Obstacle Problems
Local regularity and local boundedness results for very weak solutions of obstacle problems of the -harmonic equation
Citation: Journal of Inequalities and Applications 2010 2010:878769 -
Boundedness of Littlewood-Paley Operators Associated with Gauss Measures
Modeled on the Gauss measure, the authors introduce the locally doubling measure metric space , which means that the set
Citation: Journal of Inequalities and Applications 2010 2010:643948 -
Estimates of -Harmonic Conjugate Operator
We define the -harmonic conjugate operator and prove that f...
Citation: Journal of Inequalities and Applications 2010 2010:435450 -
Hardy-Littlewood and Caccioppoli-Type Inequalities for -Harmonic Tensors
We prove the new versions of the weighted Hardy-Littlewood inequality and Caccioppoli-type inequality for -harmonic tensors. We also exp...
Citation: Journal of Inequalities and Applications 2010 2010:351597 -
A System of Nonlinear Operator Equations for a Mixed Family of Fuzzy and Crisp Operators in Probabilistic Normed Spaces
By using a random version of the theory of contractor introduced by Altman, we introduce and study a system of nonlinear operator equations for a mixed family of fuzzy and crisp operators in probabilistic norm...
Citation: Journal of Inequalities and Applications 2010 2010:152978 -
The Convergence Rate for a -Functional in Learning Theory
It is known that in the field of learning theory based on reproducing kernel Hilbert spaces the upper bounds estimate for a -functional ...
Citation: Journal of Inequalities and Applications 2010 2010:249507 -
On Schur Convexity of Some Symmetric Functions
For and , the symmetric function ...
Citation: Journal of Inequalities and Applications 2010 2010:543250 -
On Nonhomogeneous -Harmonic Equations and 1-Harmonic Equations
We prove a characterization of a nonhomogeneous A-harmonic equation and describe its generalization. We also point out its connection with 1-Harmonic equation.
Citation: Journal of Inequalities and Applications 2010 2010:346308 -
Wiman and Arima Theorems for Quasiregular Mappings
Wiman's theorem says that an entire holomorphic function of order less than 1/2 has a minimum modulus converging to along a sequence. Arima's t...
Citation: Journal of Inequalities and Applications 2010 2010:604217 -
Nonlinear Boundary Value Problem of First-Order Impulsive Functional Differential Equations
This paper investigates the nonlinear boundary value problem for a class of first-order impulsive functional differential equations. By establishing a comparison result and utilizing the method of upper and lo...
Citation: Journal of Inequalities and Applications 2010 2010:490741 -
Weighted Inequalities for Potential Operators on Differential Forms
We develop the weak-type and strong-type inequalities for potential operators under two-weight conditions to the versions of differential forms. We also obtain some estimates for potential operators applied to...
Citation: Journal of Inequalities and Applications 2010 2010:713625 -
Poincaré Inequalities with Luxemburg Norms in -Averaging Domains
We prove both local and global Poincaré inequalities with Luxemburg norms for differential forms in -averaging domains, which can be con...
Citation: Journal of Inequalities and Applications 2010 2010:241759 -
Asymptotic Behavior of Solutions of a Periodic Diffusion Equation
We consider a degenerate parabolic equation with logistic periodic sources. First, we establish the existence of nontrivial nonnegative periodic solutions by monotonicity method. Then by using Moser iterative ...
Citation: Journal of Inequalities and Applications 2010 2010:597569 -
A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix
In the previous paper by the first and the third authors, we present six algorithms for determining whether a given symmetric matrix is strictly copositive, copositive (but not strictly), or not copositive. Th...
Citation: Journal of Inequalities and Applications 2009 2010:498631 -
General Comparison Principle for Variational-Hemivariational Inequalities
We study quasilinear elliptic variational-hemivariational inequalities involving general Leray-Lions operators. The novelty of this paper is to provide existence and comparison results whereby only a local gro...
Citation: Journal of Inequalities and Applications 2009 2009:184348