相关论文: Concentration breaking on two optimization problem…

This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates…

We show that spontaneous breaking of discrete or continuous symmetries does not necessarily imply either symmetry restoration or the thermal production of defects at high temperature (at least up to $T \sim M_{Planck}$). This may imply that…

In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on $C^{1,1}$ domains. The first one is a sharp vanishing order estimate of Robin problems with Lipschitz coefficients…

We show subellipticity of the d-bar Neumann problem on domains with Lipschitz boundary in the presence of plurisubharmonic functions with Hessians of algebraic growth. In particular, a subelliptic estimate holds near a point where the…

Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…

We prove the higher integrability of the gradient for minimizers of the thermal insulation problem, an analogue of De Giorgi's conjecture for the Mumford-Shah functional. We deduce that the singular part of the free boundary has Hausdorff…

We study the principal Dirichlet eigenfunction $\varphi_U$ when the domain $U$ is a perturbation of a bounded inner uniform domain in a strictly local regular Dirichlet space. We prove that if $U$ is suitably contained in between two inner…

We study the interior Bernoulli free boundary problem for the infinity Laplacian. Our results cover existence, uniqueness, and characterization of solutions (above a threshold representing the "infinity Bernoulli constant"), their…

We consider a second order, two-point, singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and we obtain regularity results for its solution. First we establish classical…

We prove that probability laws of certain multidimensional semimartingales which includes time-inhomogenous diffusions, under suitable assumptions, satisfy Quadratic Transportation Cost Inequality under the uniform metric. From this we…

We consider the mixed problem for $L$ the Lam\'e system of elasticity in a bounded Lipschitz domain $ \Omega\subset\reals ^2$. We suppose that the boundary is written as the union of two disjoint sets, $\partial\Omega =D\cup N$. We take…

This paper concerns with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann…

Using techniques from the analysis of PDEs to study the boundary behaviour of functions on domains with low boundary regularity, we extend results by Forna\ae{}ss-Wiegerinck (1989) on plurisubharmonic approximation and by Demailly (1987) on…

In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…

The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…

For the Alt-Caffarelli problem, we study free boundary regularity of energy minimizers. In six dimensions, we show that free boundaries are analytic for generic boundary data. In general, we improve previous generic Hausdorff dimensions of…

We study the regularity of the bounded self-similar solution to the one-phase Stefan problem with fractional diffusion posed on the whole line. In terms of the enthalpy $h(x,t)$, the evolution problem reads \[ \begin{cases} \partial_t h +…

We consider the problem of minimizing the Lagrangian $\int [F(\nabla u)+f\,u]$ among functions on $\Omega\subset\mathbb{R}^N$ with given boundary datum $\varphi$. We prove Lipschitz regularity up to the boundary for solutions of this…

We investigate the demixing dynamics in a binary two-dimensional (2D) Bose superfluid using classical-field dynamics. By quenching the interspecies interaction parameter, we identify a strong and weak separation regime depending on the…

The purpose in this paper is to determine the global behavior of solutions to the initial-boundary value problems for energy-subcritical and critical semilinear heat equations by initial data with lower energy than the mountain pass level…