146 research outputs found
On finite-difference approximations for normalized Bellman equations
A class of stochastic optimal control problems involving optimal stopping is
considered. Methods of Krylov are adapted to investigate the numerical
solutions of the corresponding normalized Bellman equations and to estimate the
rate of convergence of finite difference approximations for the optimal reward
functions.Comment: 36 pages, ArXiv version updated to the version accepted in Appl.
Math. Opti
Partial Schauder estimates for second-order elliptic and parabolic equations
We establish Schauder estimates for both divergence and non-divergence form
second-order elliptic and parabolic equations involving H\"older semi-norms not
with respect to all, but only with respect to some of the independent
variables.Comment: CVPDE, accepted (2010)
On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients
We prove the solvability in Sobolev spaces for both divergence and
non-divergence form higher order parabolic and elliptic systems in the whole
space, on a half space, and on a bounded domain. The leading coefficients are
assumed to be merely measurable in the time variable and have small mean
oscillations with respect to the spatial variables in small balls or cylinders.
For the proof, we develop a set of new techniques to produce mean oscillation
estimates for systems on a half space.Comment: 44 pages, introduction revised, references expanded. To appear in
Arch. Rational Mech. Ana
Rate of Convergence of Space Time Approximations for stochastic evolution equations
Stochastic evolution equations in Banach spaces with unbounded nonlinear
drift and diffusion operators driven by a finite dimensional Brownian motion
are considered. Under some regularity condition assumed for the solution, the
rate of convergence of various numerical approximations are estimated under
strong monotonicity and Lipschitz conditions. The abstract setting involves
general consistency conditions and is then applied to a class of quasilinear
stochastic PDEs of parabolic type.Comment: 33 page
Kernel estimates for nonautonomous Kolmogorov equations with potential term
Using time dependent Lyapunov functions, we prove pointwise upper bounds for
the heat kernels of some nonautonomous Kolmogorov operators with possibly
unbounded drift and diffusion coefficients and a possibly unbounded potential
term
Vibration Briquetting of Ash of Combined Heat and Power Plant
Ash and slag materials of combined heat and power plant (CHPP) are a unique resource that can be successfully used in construction, road and agricultural industries. However, their industrial use is accompanied with significant organizational and technical problems. Granulation of coal ashes improves the conditions of their storage and transportation, allows mechanizing and automating the subsequent use, increases productivity, improves the working conditions and reduces the loss of raw materials and finished products. This paper proposes a method of compacting of Seversk CHPP (Russia) ash by vibration briquetting using a number of binders (polyvinyl alcohol, glyoxal, liquid sodium glass). The main characteristics of Seversk CHPP ash such as chemical composition, particle size distribution, bulk density, content of unburnt carbon and radioactivity have been determined. Investigation of the effect of binder concentration on the static strength of granules revealed that the increase of binder concentration results in the growth of static strength of the dried granules that reaches a maximum at the concentration of 10 wt %: 0.28 MPa for polyvinyl alcohol, 0.63 MPa for glyoxal and 0.40 MPa for liquid sodium glass
Global estimates for solutions to the linearized Monge--Amp\`ere equations
In this paper, we establish global estimates for solutions to the
linearized Monge-Amp\`ere equations under natural assumptions on the domain,
Monge-Amp\`ere measures and boundary data. Our estimates are affine invariant
analogues of the global estimates of Winter for fully nonlinear,
uniformly elliptic equations, and also linearized counterparts of Savin's
global estimates for the Monge-Amp\`ere equations.Comment: v2: presentation improve
Well-posedness of the transport equation by stochastic perturbation
We consider the linear transport equation with a globally Holder continuous
and bounded vector field. While this deterministic PDE may not be well-posed,
we prove that a multiplicative stochastic perturbation of Brownian type is
enough to render the equation well-posed. This seems to be the first explicit
example of partial differential equation that become well-posed under the
influece of noise. The key tool is a differentiable stochastic flow constructed
and analysed by means of a special transformation of the drift of Ito-Tanaka
type.Comment: Addition of new part
Almost sure convergence of a semidiscrete Milstein scheme for SPDE's of Zakai type
A semidiscrete Milstein scheme for stochastic partial differential equations of Zakai type on a bounded domain of R^d is derived. It is shown that the order of convergence of this scheme is 1 for convergence in mean square sense. For almost sure convergence the order of convergence is proved to be 1 - e for any e > 0
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