相关论文: An Elementary Extension of Korn's First Inequality…

We prove a Korn-type inequality in H(Curl) for tensor fields.

For a bounded N-dimensional domain with Lipschitz boundary we extend Korn's first inequality to incompatible tensor fields. For compatible tensor fields our estimate reduces to a non-standard variant of the well known Korn's first…

We will prove that for piecewise smooth and concave domains Korn's first inequality holds for vector fields satisfying homogeneous normal or tangential boundary conditions with explicit Korn constant square root of 2.

We consider shells of non-constant thickness in three dimensional Euclidean space around surfaces which have bounded principal curvatures. We derive Korn's interpolation (or the so called first and a half (The inequality first introduced in…

For a bounded three-dimensional domain with Lipschitz boundary we extend Korn's first inequality to incompatible tensor fields. For compatible tensor fields our estimate reduces to a non-standard variant of the well known Korn's first…

For $n\ge2$ and $1<p<\infty$ we prove an $L^p$-version of the generalized Korn-type inequality for incompatible, $p$-integrable tensor fields $P:\Omega \to \mathbb{R}^{n\times n}$ having $p$-integrable generalized…

We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that are diffeomorphic to a circular cylindrical shell with zero…

We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequality first introduced in [6]}) and second inequalities on…

In this paper, we revisit Korn's inequality for the piecewise $H^1$ space based on general polygonal or polyhedral decompositions of the domain. Our Korn's inequality is expressed with minimal jump terms. These minimal jump terms are…

Geometric rigidity states that a gradient field which is $L^p$-close to the set of proper rotations is necessarily $L^p$-close to a fixed rotation, and is one key estimate in nonlinear elasticity. In several applications, as for example in…

The purpose of this paper is to construct a new class of discrete generalized Korn's inequalities for piecewise H2 vector fields in three-dimensional space. The resulting Korn's inequalities are different from the standard Korn's…

We give an elementary estimate that entails and generalises numerous Korn inequalities scattered in the literature. As special instances, we obtain general Korn-type inequalities involving normal or tangential trace components, or lower…

The validity of Korn's first inequality in the fractional setting in bounded domains has been open. We resolve this problem by proving that in fact Korn's first inequality holds in the case $ps>1$ for fractional $W^{s,p}_0(\Omega)$ Sobolev…

We give a new, simpler proof of the fractional Korn's inequality for subsets of $\mathbb{R}^d$. We also show a framework for obtaining Korn's inequality directly from the appropriate Hardy-type inequality.

Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large…

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are…

In this work we derive asymptotically sharp weighted Korn and Korn-like interpolation (or first and a half) inequalities in thin domains with singular weights. The constants $K$ (Korn's constant) in the inequalities depend on the domain…

We establish a family of coercive Korn-type inequalities for generalised incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several previously known inequalities that are pivotal to the…

In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shells for zero or periodic Dirichlet, Neumann, and Robin type…

We establish Korn's interpolation inequalities and the rigidity results of the strain tensor of the middle surface for the parabolic and elliptic shells and show that the best constant in Korn's inequalities scales like $h^{3/2}$ for the…