# Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations

## Related Articles

- Multiple Solutions for a Fourthâ€“order Asymptotically Linear Elliptic Problem. Ai Qian; Shu Li // Acta Mathematica Sinica;Jul2006, Vol. 22 Issue 4, p1121
Under simple conditions, we prove the existence of three solutions for a fourthâ€“order asymptotically linear elliptic boundary value problem. For the resonance case at infinity, we do not need to assume any more conditions to ensure the boundedness of the (PS) sequence of the corresponding...

- Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains. Tsing-San Hsu // Abstract & Applied Analysis;2007, p1
We will show that under suitable conditions on f and h, there exists a positive number Ï‡* such that the nonhomogeneous elliptic equation -Î”u + u = Ï‡*( f (x,u) + h(x)) in Î©, u ÎµH0Â¹ (Î©), N â‰¥ 2, has at least two positive solutions if Ï‡ Îµ (0,Ï‡*), a unique...

- Estimating the Probability of Attachment by Sliding in Flotation Modeling. Bloom, Frederick // Nonlinear Studies;2005, Vol. 12 Issue 2, p177
An iterative algorithm is constructed to compute a lower bound for the probability of adhesion by sliding which is central to modeling flotation in both deinking and mineral processing. The scheme delineated yields the value of the ratio of initial to critical film thickness which corresponds to...

- ENTIRE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS. Gladkov, Alexander; Slepchenkov, Nickolai // Electronic Journal of Differential Equations;2004, Vol. 2004, p1
We consider existence of entire solutions of a semilinear elliptic equation Î”u = k(x) f(u) for x âˆˆ Rn, n â‰¥ 3. Conditions of the existence of entire solutions have been obtained by different authors. We prove a certain optimality of these results and new sufficient conditions for...

- Maximal Inequalities for CIR Processes. Yan, Litan; Li, Yingchun // Letters in Mathematical Physics;Feb2004, Vol. 67 Issue 2, p111
Let X be a Coxâ€“Ingersollâ€“Ross (CIR) process given by$\{\backslash rm\; d\}X\_t=(a+bX\_t)\backslash ,\{\backslash rm\; d\}t+c\backslash sqrt\{\backslash vert\; X\_t\backslash vert\}\backslash ,\{\backslash rm\; d\}B\_t$with X0=0, where a, c>0, $b\backslash in\{\backslash open\; R\}$ and B a standard Brownian motion starting at zero. We obtain some inequalities between the integral...

- SchrÃ¶dinger maximal function and restriction properties of the Fourier transform. Moyua, A.; Vargas, A.; Vega, L. // IMRN: International Mathematics Research Notices;1996, Vol. 1996 Issue 16, p793
The article presents a study which aims to find enough conditions on u0 that there is convergence for nearly every x of the solution to the initial datum. The common procedure to attain the convergence is to examine the corresponding maximal function which shall be called the SchrÃ¶dinger...

- Weakly Prime Modules. Behboodi, M.; Koohy, H. // Vietnam Journal of Mathematics;Jun2004, Vol. 32 Issue 2, p185
A left R-module M is called weakly prime module if the annihilator of any nonzero submodule of M is a prime ideal and a proper submodule P of M is called weakly prime submodule if the quotient module M/P is a weakly prime module. This notion is introduced and extensively studied. The module in...

- Generalized Sobolev Classes on Metric Measure Spaces. Ivanishko, I. A. // Mathematical Notes;May/Jun2005, Vol. 77 Issue 5/6, p865
This article presents a paper, which gives several descriptions in different terms--via maximal functions, the Poincare inequality and so on--of generalized classes of Sobolev type on metric measure spaces. At present, there exist a number of different approaches to the definition of such...

- Weighted inequalities for the generalized maximal operator in martingale spaces. Chen, Wei; Liu, Peide // Chinese Annals of Mathematics;Sep2011, Vol. 32 Issue 5, p781
The generalized maximal operator M in martingale spaces is considered. For 1 < p â‰¤ q < âˆž, the authors give a necessary and sufficient condition on the pair ( $\hat \mu $, v) for M to be a bounded operator from martingale space L( v) into L( $\hat \mu $) or weak- L ( $\hat \mu $),...