TITLE

# New Korn-type inequalities and regularity of solutions to linear elliptic systems and anisotropic variational problems involving the trace-free part of the symmetric gradient

AUTHOR(S)
Schirra, Oliver
PUB. DATE
January 2012
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2012, Vol. 43 Issue 1/2, p147
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The aim of this note is to investigate a regularity theory for minimizers of energies whose density depends on the trace-free part of the symmetric gradient, where integrands of anisotropic growth are considered. An adequate coercive inequality guarantees the existence of minimizers of such energies in suitable Sobolev classes. Moreover, various other Korn-type inequalities are shown, which can be used to prove the smoothness of weak solutions to linear elliptic systems involving the trace-free part of the symmetric gradient. In particular, Campanato-type estimates for solutions to such systems are established so that all tools are available to prove the interior regularity of minimizers of energies depending on the trace-free part of the symmetric gradient.
ACCESSION #
67363483

## Related Articles

• On the symmetric Laplace derivative. Garai, A.; Ray, S. // Acta Mathematica Hungarica;Oct2011, Vol. 133 Issue 1/2, p166

Let f: R? R be integrable in a neighbourhood of x? R. If there are real numbers a, a,..., a such that exists for some d>0 then the limit is called the 2 n-th symmetric Laplace derivative at x. There is a corresponding definition of (2 n+1)-th symmetric Laplace derivative. It is shown that this...

• Bell's theorem with no locality assumption: putting free will at work. Tresser, C. // European Physical Journal D -- Atoms, Molecules, Clusters & Opti;Mar2011, Vol. 62 Issue 1, p139

We prove a version of Bell's Theorem which does not assume Locality but instead only the conjunction of a Free Will Principle (so weak that one's will needs not be free from one's past) and what we call the Effect After Cause Principle (EACP) according to which for any Lorentz observer the value...

• CALCULATION OF SOME TOPOLOGICAL INDICES OF GRAPHS. ESSALIH, MOHAMED; EL MARRAKI, MOHAMED; EL HAGRI, GABER // Journal of Theoretical & Applied Information Technology;2011, Vol. 30 Issue 2, p122

In this paper, we give some theoretical results, for the index Wiener, degree distance and the hyper-Wiener index of a graphG, according to dG(k)(The number of pairs of vertices of G that are at distance), and the diameter of G. We accomplish this by firstly, giving another proof of the...

• A Higher-Order Hardy-Type Inequality in Anisotropic Sobolev Spaces. Secchi, Paolo // International Journal of Differential Equations;2012, p1

We prove a higher-order inequality of Hardy type for functions in anisotropic Sobolev spaces that vanish at the boundary of the space domain. This is an important calculus tool for the study of initial-boundary-value problems of symmetric hyperbolic systems with characteristic boundary.

• Complete Consistency of the Estimator of Nonparametric Regression Models Based on ...-Mixing Sequences. Xuejun Wang; Fengxi Xia; Meimei Ge; Shuhe Hu; Wenzhi Yang // Abstract & Applied Analysis;2012, p1

We study the complete consistency for estimator of nonparametric regression model based on ...-mixing sequences by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained.

• Monotonicity and one-dimensional symmetry for solutions of -? u = f( u) in half-spaces. Farina, Alberto; Montoro, Luigi; Sciunzi, Berardino // Calculus of Variations & Partial Differential Equations;Jan2012, Vol. 43 Issue 1/2, p123

We prove a weak comparison principle in narrow domains for sub-super solutions to -? u = f( u) in the case 1 < p = 2 and f locally Lipschitz continuous. We exploit it to get the monotonicity of positive solutions to -? u = f( u) in half spaces, in the case $${\frac{2N+2}{N+2} < p\leq 2}$$ and f...

• Inequalities for Partial Moduli of Continuity and Partial Derivatives. Kolyada, V.; Pérez Lázaro, F. // Constructive Approximation;Aug2011, Vol. 34 Issue 1, p23

We obtain pointwise and integral type estimates of higher-order partial moduli of continuity in C via partial derivatives. Also, a Gagliardo-Nirenberg type inequality for partial derivatives in a fixed direction is proved. Our methods enable us to study the case when different partial...

• Univariate mixed Caputo fractional Ostrowski inequalities. Anastassiou, George A. // Journal of Computational Analysis & Applications;May2012, Vol. 14 Issue 4, p706

Very general univariate mixed Caputo fractional Ostrowski inequalities are presented. One of them is proved sharp and attained. Estimates are with respect to ||Â· ||p, 1 â‰¤ v â‰¤ *infin;.

• Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means. Qian, Wei-Mao; Shen, Zhong-Hua // Journal of Applied Mathematics;2012, p1

We prove that aH(a, b) + (1 - a)L(a, b) > M(1-4a)/3(a, b) for a âˆŠ (0, 1) and all a, b > 0 with aâ‰„ b if and only if a âˆŠ [1/4, 1] and aH(a, b) + (1 - a)L(a, b) < M(1-4a)/3(a, b) if and only if a âˆŠ (0, 3 v345/80 - 11/16), and the parameter (1 - 4a)/3 is the best possible in...

Share