I need an estimate for $\| \nabla w\|_{L^2{(\Omega \subset \mathbb{R}^n)}}$, such that it is $< c\| w\|,\ w \in H_0^1(\Omega)\ $. Is this possible?
Inverse estimate of gradient of Sobolev function
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sobolev-spaces
estimation
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1What do you mean by $\|w\|$? Is it the $H^1_0$ norm or the $L^2$ norm of $w$? – 2012-11-19
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0It is the $L^2$-norm. – 2012-11-19