# 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

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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...

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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...

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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...