Related papers: Bounds on the Trace Mappings of LD-Fields

A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on…

In this article, we develop the theory of weighted $L^2$ Sobolev spaces on unbounded domains in $\mathbb R^n$. As an application, we establish the elliptic theory for elliptic operators and prove trace and extension results analogous to the…

We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball.

We use ab initio local stress calculations to investigate layer-by-layer ab initio stress inside late transition metal (111) surfaces, focusing on the origin of stress on the surface top layer. It is found that the band shift on each…

We prove that given any positive integer $k$, for each open set $\Omega$ and any closed subset $D$ of its closure such that $\Omega$ is locally an (epsilon,delta)-domain near points in the boundary of $\Omega$ not contained in $D$ there…

In this paper, we study the critical Sobolev embeddings $W^{1,p(x)}(\Omega)\subset L^{p^*(x)}(\Omega)$ for variable exponent Sobolev spaces from the point of view of the $\Gamma$-convergence. More precisely we determine the $\Gamma$-limit…

This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…

We study the Sobolev trace constant for functions defined in a bounded domain $\O$ that vanish in the subset $A.$ We find a formula for the first variation of the Sobolev trace with respect to hole. As a consequence of this formula, we…

We characterize the real interpolation space between a weighted $L^p$ space and a weighted Sobolev space in arbitrary bounded domains in $\mathbb{R}^n$, with weights that are positive powers of the distance to the boundary.

We prove sharp embedding inequalities for certain reduced Sobolev spaces that arise naturally in the context of Dirichlet problems with $L^1$ data. We also find the optimal target spaces for such embeddings, which in dimension 2 could be…

Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional…

We study the approximative trace for individual elements in the Sobolev space $W^{1,p}(\Omega)$ for $1\le p\le\infty$. This notion of a trace was introduced for $p=2$ in [AtE11] in the setting of general open sets…

Strain has been extensively employed to tailor graphene's properties and has emerged as a powerful tool for engineering gauge fields and exploring fundamental phenomena in artificial platforms like photonic graphene. Here we discover that,…

Let $\Sigma\subset\mathbb{R}^d$ be a $C^\infty$-smooth closed compact hypersurface, which splits the Euclidean space $\mathbb{R}^d$ into two domains $\Omega_\pm$. In this note self-adjoint Schr\"odinger operators with $\delta$ and…

In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the real line, and also a one-dimensional version of the well-known Poincare inequality.

There are known trace and extension theorems relating functions in a weighted Sobolev space in a domain U to functions in a Besov space on the boundary bU. We extend these theorems to the case where the Sobolev exponent p is less than one…

In this paper, we consider a maximizing problem associated with the Sobolev type embedding on the space of bounded variation. We show that, although the maximizing problem suffers from both of the non-compactness of vanishing and…

The force fields of interior boundaries of matters are calculated as superposition of fields of modified Sierpinski carpet. The long-range effect interaction in irradiated crystals is introduced as various manifestations of second order…

We study homogenisation problems for divergence form equations with rapidly sign-changing coefficients. With a focus on problems with piecewise constant, scalar coefficients in a ($d$-dimensional) crosswalk type shape, we will provide a…