An approximation result for solutions of Hessian equations

Urbas, John
June 2007
Calculus of Variations & Partial Differential Equations;Jun2007, Vol. 29 Issue 2, p219
Academic Journal
We show that W 2, p weak solutions of the k-Hessian equation F k ( D 2 u) = g( x) with k≥ 2 can be approximated by smooth k-convex solutions v j of similar equations with the right hands sides controlled uniformly in C 0,1 norm, and so that the quantities $$ \int_{B_r} (\Delta v_j)^{p-k+1} F_{k-1}(D^2v_j) $$ are bounded independently of j. This result simplifies the proof of previous interior regularity results for solutions of such equations. It also permits us to extend certain estimates for smooth solutions of degenerate two dimensional Monge–Ampère equations to W 2, p solutions.


Related Articles

  • Use of Welch-Satterthwaite Approximation in Calibration of Voltage Standards. Crowder, Stephen V.; Kupferman, Stuart L. // Journal of Quality Technology;Jan2004, Vol. 36 Issue 1, p38 

    In certifying banks of solid state voltage standards, the customer is provided with predictive equations that are used to predict mean voltage and uncertainty in voltage. These equations are provided for both the bank average and the individual standards constituting the bank over the period of...

  • Research on AMSAA-BISE model�An answer to Mei Men-Hua. Zhou Yuan-quan // Applied Mathematics & Mechanics;Jul2001, Vol. 22 Issue 7, p856 

    The AMSAA-BISE model is derived from another approach. This certainly shows the correctness of the AMSAA-BISE model, and indicates the incorrectness of the approximate model given in this paper. The engineering example illustrating these conclusions is given. Merits and demerits of AMSAA and...

  • Consistent initialization and perturbation analysis for abstract differential-algebraic equations. Reis, Timo // Mathematics of Control, Signals & Systems;Sep2007, Vol. 19 Issue 3, p255 

    In this paper, we consider linear and time-invariant differential-algebraic equations (DAEs) E?( t) = Ax( t) + f( t), x(0) = x 0, where x(�) and f(�) are functions with values in Hilbert spaces X and Z. $${E : X \to Z}$$ is assumed to be a bounded operator, whereas A is closed and...

  • Quadratic estimates and functional calculi of perturbed Dirac operators. Axelsson, Andreas; Keith, Stephen; McIntosh, Alan // Inventiones Mathematicae;Mar2006, Vol. 163 Issue 3, p455 

    We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge�Dirac operator on compact manifolds depend analytically on L 8 changes in...

  • Numerical quenching for a nonlinear diffusion equation with a singular boundary condition. Nabongo, Diabate; Boni, Th�odore K. // Bulletin of the Belgian Mathematical Society - Simon Stevin;May2009, Vol. 16 Issue 2, p289 

    This paper concerns the study of the numerical approximation for the following boundary value problem { (um)t = uxx, 0 < x < 1, t > 0, ux(0, t) = 0, ux(1, t) = -u-�(1, t), t > 0, u(x, 0) = u0(x) > 0, 0 = x = 1, where m = 1, � > 0. We obtain some conditions under which the solution of a...

  • GENERALIZED S--SHAPEDNESS OF RELIABILITY FUNCTIONS. Pilpel, Shaiy // Mathematics of Operations Research;Aug86, Vol. 11 Issue 3, p433 

    Reliability functions have the property that if they intersect the diagonal y = x it is done in an S-shaped form (Moore and Shannon). In this paper a wider class of polynomials is presented, the members of which form a dense grid on the unit square. The S-shapedness intersection property holds...

  • The Euler—Poisson System in 2D: Global Stability of the Constant Equilibrium Solution. Ionescu, Alexandru D.; Pausader, Benoit // IMRN: International Mathematics Research Notices;Feb2013, Vol. 2013 Issue 4, p761 

    We consider the (repulsive) Euler–Poisson system for the electrons in two dimensions and prove that small smooth perturbations of a constant background exist for all time and remain smooth (never develop shocks). This extends to 2D the work of Guo 6.

  • Approximation of Functions with Singularities by Truncated Bernstein Operators. Dansheng Yu; Dejun Zhao // Southeast Asian Bulletin of Mathematics;2006, Vol. 30 Issue 6, p1169 

    We construct a kind of truncated Bernstein operators to approximate functions with singularities. The approximation rate is also investigated.

  • On Controllability of Structures with Closely Spaced Natural Frequencies Based on Perturbation Analysis. Xie Faxiang; Sun Limin // AIP Conference Proceedings;5/21/2010, Vol. 1233 Issue 1, p753 

    His paper investigated the influence of frequency intensity parameters on the controllability of structures with closely-spaced natural frequencies. The perturbation equations were established for a closed-loop system to study the relationship between frequencies, mode damping ratios and...


Read the Article


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

Try another library?
Sign out of this library

Other Topics