Related papers: Elementary numerical methods for double integrals
We consider weak solutions of the adjoint equation for an elliptic operator in nondivergent form, and their asymptotic properties at an interior point. We assume that the coefficients a_{ij} are bounded, measurable, complex-valued functions…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
We prove L^p estimates for a class of two-dimensional multilinear forms that naturally generalize (dyadic variants of) both classical paraproducts and the twisted paraproduct introduced in [5] and studied in [1] and [6]. The method we use…
We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449--1466]. For a given semi-rational…
This paper is concerned with proving some embeddings of the form \begin{equation*} F_{p_{1},q}^{s_{1}}\cdot B_{p_{2},\infty }^{s_{2}}\cdot ...\cdot B_{p_{m},\infty }^{s_{m}}\hookrightarrow F_{p,q}^{s_{1}},\quad m\geq 2. \end{equation*} The…
We establish two new estimates which control a function (after subtracting its average) in $L^1$ by only the $L^1$ norm of its radial derivative. While the interior estimate holds for all superharmonic functions, the boundary version is…
Based on a new Taylor-like formula, we derived an improved interpolation error estimate in $W^{1,p}$. We compare it with the classical error estimates based on the standard Taylor formula, and also with the corresponding interpolation error…
We find estimates on the norms commutators of the form [f(x), y] in terms of the norm of [x, y] assuming that x and y are contractions in a C*-algebra A, with x normal and with spectrum within the domain of f. In particular we discuss [x^2,…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are P-functions. Some applications to special means of real…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier integral. The double exponential transformation is not only useful for numerical computations but it is…
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
We show $L^p$ estimates for square roots of second order complex elliptic systems $L$ in divergence form on open sets in $\mathbb{R}^d$ subject to mixed boundary conditions. The underlying set is supposed to be locally uniform near the…
The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a…
In order to study Fractional operator, Caffarelli introduced the concept of extension problem. Hence, for any fractional elliptic operator, we get a degenerate elliptic equation. By studying the W^{1,p} regularity of extension problem, we…
For functions from the set of generalized Poisson integrals $C^{\alpha,r}_{\beta}L_{p}$, $1\leq p <\infty$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the…
We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses St\"urmer's extrapolation formula and assumes…
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
Using fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued H\"{o}lder continuous functions of order $\displaystyle \beta \in (\frac13, \frac12)$ and $f$ is a continuously…
We present and analyse numerical quadrature rules for evaluating regular and singular integrals on self-similar fractal sets. The integration domain $\mathbb{R}^n$ is assumed to be the compact attractor of an iterated function system of…
We provide a higher integrability result for the gradient of positive solutions to Trudinger's equation (also known as the doubly non-linear equation) for the range $p\in [2,\infty)$. The estimate is achieved by refining a construction of…