相关论文: Uniform estimates: from Yau to Kolodziej
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
In this article, we introduce and study three numerical methods for the Dirichlet Monge Amp\`ere equation in two dimensions. The approaches consist in considering new equivalent problems. The latter are discretized by a wide stencil finite…
In this paper we consider Yamabe type problem for higher order curvatures on manifolds with totally geodesic boundaries. We prove local gradient and second derivative estimates for solutions to the fully nonlinear elliptic equations…
A generalized matrix-pencil approach is proposed for the estimation of complex exponential components with segmented signal samples, which is very efficient and provides super-resolution estimations. It is applicable to the signals sampled…
We present a Chebyshev collocation method for linear ODE and DDE problems. We first give a posteriori estimates for the accuracy of the approximate solution of a scalar ODE initial value problem. Examples of the success of the estimate are…
We consider the uniform resolvent and orthonormal Strichartz estimates for the Schr\"odinger operator. First we prove the Keel-Tao type theorem for the orthonormal Strichartz estimates, which means that the dispersive estimates yield the…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed…
We prove existence and regularity of entire solutions to Monge-Ampere equations invariant under an irreducible action of a compact Lie group.
We consider a solution to a parametric family of the Cauchy problems for $m$th-order linear differential equations with constant coefficients. Parameters of the family are the coefficients of the differential equation and the initial values…
We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretisation errors…
We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.
We study a Monge-Amp\`{e}re equation with power term for some $p\in{\mathbb{R}}$. A solution $u$ is called to be Euclidean complete if it is an entire solution defined over the whole ${\mathbb{R}}^n$ or its graph is a large hypersurface…
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic…
One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…
We derive a formula for non-Archimedean Monge-Amp\`{e}re measures of big models. As applications, we derive a positive intersection formula for non-Archimedean Mabuchi functional, and further reduce the uniform Yau-Tian-Donaldson conjecture…
We prove that positive solutions of the Lane-Emden equation in a two-dimensional smooth bounded domain are uniformly bounded for all large exponents.
We describe a method to reduce partial differential equations of Monge-Amp\`ere type in 4 variables to complex partial differential equations in 2 variables. To illustrate this method, we construct explicit holomorphic solutions of the…
The aim of this article is to give a method to construct bimodule resolutions of associative algebras, generalizing Bardzell's well-known resolution of monomial algebras. We stress that this method leads to concrete computations, providing…
The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Amp\`ere type known as generated Jacobian equations. These equations, whose general existence theory has been recently…