Related papers: Gradient estimates for the insulated conductivity …

This paper presents two approaches to the precise design of maximally flat antireflection coatings reducing the reflectance of the substrate to near zero in a certain region around the central frequency. The first ideal case concerns…

In this paper, we will use the maximum principle to give a new proof of the gradient estimates for mean curvature equations with some oblique derivative problems. Specially, we shall give a new proof for the capillary problem with zero…

In the paper, we establish a blow-up criterion in terms of the integrability of the density for strong solutions to the Cauchy problem of compressible isentropic Navier-Stokes equations in \mathbb{R}^3 with vacuum, under the assumptions on…

The gradients of convex functions are expressive models of non-trivial vector fields. For example, Brenier's theorem yields that the optimal transport map between any two measures on Euclidean space under the squared distance is realized as…

We prove a generic flatness result for the cohomology of thickenings of a projective scheme that is smooth over a Noetherian domain containing a field of characteristic zero. Our study is motivated, in part, by a classical question in…

Many engineering applications can be formulated as optimizations constrained by conservation laws. Such optimizations can be efficiently solved by the adjoint method, which computes the gradient of the objective to the design variables.…

We use holography to compute the conductivity in an inhomogeneous charged scalar background. We work in the probe limit of the four-dimensional Einstein-Maxwell theory coupled to a charged scalar. The background has zero charge density and…

We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary…

We consider the diffusive Hamilton-Jacobi equation, with homogeneous Dirichlet conditions and regular initial data. It is known from [Barles-DaLio, 2004] that the problem admits a unique, continuous, global viscosity solution, which extends…

We present a comprehensive study of the reflection of normally incident plasmon waves from a low-conductivity 1D junction in a 2D conductive sheet. Rigorous analytical results are derived in the limits of wide and narrow junctions. Two…

The stress concentration is a common phenomenon in the study of fluid-solid model. In this paper, we investigate the boundary gradient estimates and the second order derivatives estimates for the Stokes flow when the rigid particles…

We concider, the blow-up solutions for a coupled reaction diffusion system with gradient terms. The main purpose is to understand whether the gradient terms effect the blow-up properties. We derive the upper and lower blow-up rate estimates…

We study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscous compressible fluids without heat conduction will blow up…

We establish the a priori estimates and prove a blow-up criterion for the three-dimensional free boundary incompressible ideal magnetohydrodynamics equations. The fluid occupies a bounded region with a free boundary that is a closed…

We consider non-local in time semilinear subdiffusion equations on a bounded domain, where the kernel in the integro-differential operator belongs to a large class, which covers many relevant cases from physics applications, in particular…

We study the minimum number of inflection points among generic immersed closed plane curves with a fixed embedded shadow. The word immersed is essential: a genuinely embedded Jordan curve has inflection minimum zero. For tree-like shadows,…

This article is concerned with a semilinear time-fractional diffusion equation with a superlinear convex semilinear term in a bounded domain $\Omega$ with the homogeneous Dirichlet, Neumann, Robin boundary conditions and non-negative and…

We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…

The study of blow-up solution of time-fractional heat equations is of significant and wide-ranging interest for its multitude of applications. These types of equations are used to model several real problems in science and engineering. This…

In this paper, we consider the Schr\"odinger equation with a mass-supercritical focusing nonlinearity, in the exterior of a smooth, compact, convex obstacle of $\R^{d}$ with Dirichlet boundary conditions. We prove that solutions with…