相关论文: Convergence of numerical approximations to non-lin…
We prove compactness and hence existence for solutions to a class of non linear transport equations. The corresponding models combine the features of linear transport equations and scalar conservation laws. We introduce a new method which…
We investigate the properties of discretizations of advection equations on non-cartesian grids and graphs in general. Advection equations discretized on non-cartesian grids have remained a long-standing challenge as the structure of the…
In this paper we analyse the selection problem for weak solutions of the transport equation with rough vector field. We answer in the negative the question whether solutions of the equation with a regularized vector field converge to a…
We prove existence of solutions to a nonlinear transport equation in the plane, for which the velocity field is obtained as the convolution of the classical Cauchy Kernel with the unknown. Even though the initial datum is bounded and…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
We study the entropic regularizations of optimal transport problems under suitable summability assumptions on the point-wise transport cost. These summability assumptions already appear in the literature. However, we show that the weakest…
In this paper we prove a nonlocal version of the Cordes-Niremberg estimates. We use it to extend our previous regularity results for fully nonlinear integro-differential equations to the variable coefficient case and several other settings…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…
The pure traction problem of elasticity appears frequently in engineering applications, and its complexity stems from the fact that its solution is unique only up to (infinitesimal) rigid body motions. When finite elements are employed to…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau \cite{bernardeau92}, Gramann…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
Given $k:\mathbb{R}^n\setminus\{0\} \to \mathbb{R}^n$ a kernel of class $C^2$ and homogeneous of degree $1-n$, we prove existence and uniqueness of H\"older regular solutions for some non-linear transport equations with velocity fields…
We prove the persistence of boundary smoothness of vortex patches for a non-linear transport equation in $\mathbb{R}^n$ with velocity field given by convolution of the density with an odd kernel, homogeneous of degree $-(n-1)$ and of class…
The purpose of this article is to solve rough differential equations with the theory of regularity structures. These new tools recently developed by Martin Hairer for solving semi-linear partial differential stochastic equations were…