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- W2792668716 abstract "We obtain the inequality begin{multline*} int_{Omega}|nabla u(x)|^ph(u(x))dx leq C(n,p)int_{Omega} Big( sqrt{ |nabla^{(2)} u(x)||{mathcal T}_{h,C}(u(x))|}Big)^{p}h(u(x))dx, end{multline*} where $Omegasubset mathbb R^n$ and $nge 2$, $ucolonOmegarightarrow mathbb R$ is in certain subset in second order Sobolev space $W^{2,1}_{rom{loc}}(Omega)$, $nabla^{(2)} u$ is the Hessian matrix of $u$, ${mathcal T}_{h,C}(u)$ is a certain transformation of the continuous function $h(cdot)$. Such inequality is the generalization of a similar inequality holding in one dimension, obtained earlier by second author and Peszek." @default.
- W2792668716 created "2018-03-29" @default.
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- W2792668716 date "2018-03-18" @default.
- W2792668716 modified "2023-09-26" @default.
- W2792668716 title "On certain variant of strongly nonlinear multidimensional interpolation inequality" @default.
- W2792668716 doi "https://doi.org/10.12775/tmna.2017.050" @default.
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