相关论文: Optimal Approximation of Elliptic Problems by Line…
In this work we establish the optimal regularity for solutions to the fully nonlinear thin obstacle problem. In particular, we show the existence of an optimal exponent $\alpha_F$ such that $u$ is $C^{1,\alpha_F}$ on either side of the…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
The paper aims at constructing two different solutions to an elliptic system $$ u \cdot \nabla u + (-\Delta)^m u = \lambda F $$ defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers…
This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first…
We study fully discrete linearized Galerkin finite element approximations to a nonlinear gradient flow, applications of which can be found in many areas. Due to the strong nonlinearity of the equation, existing analyses for implicit schemes…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
We consider the homogenization of a semilinear elliptic equation where the coefficients of the second-order differential operator may be discontinuous. We establish the existence and uniqueness of the fine-scale solution, followed by an a…
In practice, most of the optimization problems are non-linear requiring certain interactive solutions and approaches to model. In 5G Advanced and Beyond network slicing, mathematically modeling the users, type of service distributions and…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
This paper presents a Fourier integral pseudospectral (FIPS) method for a general class of nonlinear, periodic optimal control (OC) problems with equality and/or inequality constraints and sufficiently smooth solutions. In this scheme, the…
We establish optimal L^p bounds for the nontangential maximal function of the gradient of the solution to a second order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the…
Given a set of points in the plane, the \textsc{General Position Subset Selection} problem is that of finding a maximum-size subset of points in general position, i.e., with no three points collinear. The problem is known to be ${\rm…
This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
Corrector estimates constitute a key ingredient in the derivation of optimal convergence rates via two-scale expansion techniques in homogenization theory of random uniformly elliptic equations. The present work follows up - in terms of…
It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations…
The problem of measuring the best linear approximation of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
In this paper, we propose an approximation method to study the regularity of solutions to the Isaacs equation. This class of problems plays a paramount role in the regularity theory for fully nonlinear elliptic equations. First, it is a…
In this paper we extend recent developments in computational optimal transport to the setting of Riemannian manifolds. In particular, we show how to learn optimal transport maps from samples that relate probability distributions defined on…