相关论文: On weak solutions for fourth-order problems involv…
Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…
We prove existence of weak solutions to an evolutionary model derived for magnetoelastic materials. The model is phrased in Eulerian coordinates and consists in particular of (i) a Navier-Stokes equation that involves magnetic and elastic…
The paper is concerned with the weak convergence of $n$-particle processes to deterministic stationary paths as $n\to\infty$. A Mosco type convergence of a class of bilinear forms is introduced. The Mosco type convergence of bilinear forms…
We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solutions to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their…
In this paper, we give a formulation of the variational iteration method that makes it suitable for the analysis of the solutions of Klein-Gordon equations with variable coefficients. We particularly study a Klein-Gordon problem which has…
In this article, the structure of the incremental quasistatic contact problem with Coulomb friction in linear elasticity (Signorini-Coulomb problem) is unraveled and sharp existence results are proved for the most general two-dimensional…
In this paper, we establish the existence and uniqueness of weak solutions to first-order discount mean field games and a stability result to give the existence for the ergodic problem. We show an example to illustrate the multiplicity of…
In the present paper, we study a double-phase variable exponent problem which is set up within a variational framework including a singular potential of fractional-Hardy-type. We employ the Mountain-Pass theorem and the strong minimum…
We investigate an evolutive system of non-linear partial differential equations derived from Oldroyd models on Non-Newtonian flows. We prove global existence of weak solutions, in the case of a smooth bounded domain, for general initial…
After different variables and functions changes, the generalized dispersal problem, recalled in (1) below and considered in part I, see Labbas, Maingot and Thorel [14], leads us to consider, to study and to invert the sum of linear…
Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
This paper is a continuation of the recent work of Guo-Xiang-Zheng \cite{Guo-Xiang-Zheng-2021-CV}. We deduce sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivi\`ere equation \begin{equation*}…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and…
In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…
We study porous medium equations with a divergence form of drift terms in a bounded domain with no-flux lateral boundary conditions. We establish $L^q$-weak solutions for $ 1\leq q < \infty$ in Wasserstein space under appropriate conditions…
By means of variational methods we investigate existence, non-existence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacian operator and with nonlinearity reaching the critical…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…