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- W2950578061 abstract "We will prove a global estimate for the gradient of the solution to the {it Poisson differential inequality} $|Delta u(x)|le a|nabla u(x)|^2+b$, $xin B^{n}$, where $a,b<infty$ and $u|_{S^{n-1}}in C^{1,alpha}(S^{n-1}, Bbb R^m)$. If $m=1$ and $ale (n+1)/(|u|_infty4nsqrt n)$, then $|nabla u| $ is a priori bounded. This generalizes some similar results due to E. Heinz (cite{EH}) and Bernstein (cite{BS}) for the plane. An application of these results yields the theorem, which is the main result of the paper: A quasiconformal mapping of the unit ball onto a domain with $C^2$ smooth boundary, satisfying the Poisson differential inequality, is Lipschitz continuous. This extends some results of the author, Mateljevi'c and Pavlovi'c from the complex plane to the space." @default.
- W2950578061 created "2019-06-27" @default.
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- W2950578061 date "2007-12-21" @default.
- W2950578061 modified "2023-09-27" @default.
- W2950578061 title "A priori estimate of gradient of a solution to certain differential inequality and quasiconformal mappings" @default.
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