Related papers: Bellman function for extremal problems in BMO
In this paper we study the $p$-Poisson equation with Robin boundary conditions, where the Robin parameter is a function. By means of some weighted isoperimetric inequalities, we provide various sharp bounds for the solutions to the problems…
We get sharp estimates for the distribution function of nonnegative weights, which satisfy so called $A_{p_1, p_2}$ condition. For particular choices of parameters $p_1$, $p_2$ this condition becomes an $A_p$-condition or Reverse H\"{o}lder…
We look for pointwise bounds on a plurisubharmonic function near its singularity point, given the value of its generalized Lelong number with respect to a plurisubharmonic weight. To this end, an extremal problem is considered. In certain…
The paper contains the proof of $L^p$-weighted norm inequalities for both, martingales square functions and the classical square functions in harmonic analysis of Littlewood-Paley and Lusin. Furthermore, the bounds are completely explicit…
This paper introduces a set of algorithms for Monte-Carlo Bayesian reinforcement learning. Firstly, Monte-Carlo estimation of upper bounds on the Bayes-optimal value function is employed to construct an optimistic policy. Secondly,…
We give a new probabilistic construction of solutions to real Monge-Amp\`ere equations in R^n satisfying the second boundary value problem with respect to a given target convex body P) which fits naturally into the theory of optimal…
In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…
In this paper we prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted $L^p$…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
In this article, we address endpoint issues for the bilinear spherical maximal functions. We obtain borderline restricted weak type estimates for the well studied bilinear spherical maximal function…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
We prove a sharp version of the Hopf boundary point lemma for Black-Scholes type equations. We also investigate the existence and the regularity of the spatial derivative of the solutions at the spatial boundary.
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
In this paper, we investigate the problem of nonparametric monotone frontier estimation from the perspective of extreme value theory. This enables us to revisit the asymptotic theory of the popular free disposal hull estimator in a more…
We review recent advances in the numerical analysis of the Monge-Amp\`ere equation. Various computational techniques are discussed including wide-stencil finite difference schemes, two-scaled methods, finite element methods, and methods…
We consider a Monge-Amp\`ere functional and its corresponding second boundary value problem, a nonlinear fourth order PDE with two Dirichlet boundary conditions. This problem was solved by Trudinger-Wang and Le under the assumption that the…
This paper systematically studies Hilbert boundary value problems for hyper monogenic functions on the hyperplane for the solutions being of any integer orders at the infinity, where the negative order cases are new even when restricted to…
We study solution techniques for elliptic equations in divergence form, where the coefficients are only of bounded mean oscillation (BMO). For $|p-2|<\varepsilon$ and a right hand side in $W^{-1}_p$ we show convergence of a finite element…
In this paper, we consider the global regularity for Monge-Amp\`ere type equations with the Neumann boundary conditions on Riemannian manifolds. It is known that the classical solvability of the Neumann boundary value problem is obtained…
We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE. The main idea is to repeatedly solve its linearization by using the quasi-reversibility…