# Tagged Questions

71 views

### Estimate divergence by gradient in H1

I am currently trying to fully understand the stationary Stokes equations of incompressible fluid. In the mixed form (homogeneous boundary data), for $\Omega\subset\mathbb{R}^d$, $d\in\{2,3\}$, a ...
57 views

I consider the inequality as follows: let $a>0,b>0$, and satisfy $$2a^2-b^2\leq C(1+a).\tag{1}$$ If we assume that $b\leq a$, then there exist a constant $C_1>0$ such that $$a\leq ... 1answer 184 views ### Interpret the terms in Strang's second lemma The second lemma of Strang states that for a certain choice of V_h, a, u and f there exists a c>0 such that$$||u-u_h|| \leq c (\inf_{v\in V_h} ||u-v|| + \sup_{v\in V_h} ...
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?
Lemma 3.3 Suppose $u \in H^{1}(\Omega)$ satisfies $$\int_{B_r(x_0)}|Du|^2 \le M r^{^\mu} \quad \mbox{for any} \ \ B_r(x_0) \subset \Omega,$$ for some $\mu \in [0,n)$. Then, for any \$\Omega' ...