相关论文: Weak uniqueness and partial regularity for the com…

We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…

We prove a $\Gamma$-convergence result for space dependent weak membrane energies, that is for 'truncated quadratic potentials', that are quadratic below some threshold (depending on the pair of points that we are considering) and constant…

The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied. We prove a well-posedeness of linear problem and optimal regularity result for the nonlinear problem which occur in fluid…

We consider parabolic systems in divergence form with piecewise $C^{(s+\delta)/2,s+\delta}$ coefficients and data in a bounded domain consisting of a finite number of cylindrical subdomains with interfacial boundaries in $C^{s+1+\mu}$,…

In this paper, we develop an analytical framework for the partial differential equation underlying the consensus-based optimization model. The main challenge arises from the nonlinear, nonlocal nature of the consensus point, coupled with a…

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…

Let $(M^n,g,e^{-\phi}dV_g,e^{-\phi}dA_g,m)$ be a compact smooth metric measure space with boundary with $n\geqslant 3$. In this article, we consider several Yamabe-type problems on a compact smooth metric measure space with or without…

We prove optimal regularity and a detailed analysis of the free boundary of the solutions to the thin obstacle problem for nonparametric minimal surfaces with flat obstacles.

This article deals with the variable coefficient thin obstacle problem in $n+1$ dimensions. We address the regular free boundary regularity, the behavior of the solution close to the free boundary and the optimal regularity of the solution…

We study the regularity of free boundaries in the multiple elastic membrane problem in the plane. We prove the uniqueness of blow-ups, and that the free boundaries are $C^{1,\log}$-curves near a regular intersection point.

We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions…

In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modelling…

We prove some regularity results for a connected set S in the planar domain O, which minimizes the compliance of its complement O\S, plus its length. This problem, interpreted as to find the best location for attaching a membrane subject to…

We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that…

In this article we exploite the uniform decay for damped linear wave equation with Zaremba boundary condition, obtained in a previous work, to treat the same problem in nonlinear context. We need a uniqueness assumption, usual for this type…

Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…

We would like to study a weakly coupled system of semi-linear classical damped wave equations with moduli of continuity in nonlinearities whose powers belong to the critical curve in the $p-q$ plane. The main goal of this paper is to find…

In this paper we study the existence and partial regularity of weak solutions to an elliptic-parabolic system that models the single-phase miscible displacement of one incompressible fluid by another in a porous media. The system is…

We give a blow-up behavior for solutions to a problem with singularity and with Dirichlet condition. An application, we have a compactness of the solutions to this Problem with singularity and Lipschitz conditions.

We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of…