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1d
answered Variant of Ladyzhenskaya’s inequality
1d
comment Variant of Ladyzhenskaya’s inequality
Note that $(x+y)^2\le 2x^2+2y^2$.
2d
comment Prove difference quotient converges to weak derivative in $L^p$
In this case, you can adapt the proof given by @Jose27, which is now deleted.
Apr
14
comment Question about representation of the eigenvalues of second order elliptic operator
Have you tried to prove it?
Apr
11
comment The Courant Min-Max theorem of elliptic pdes.
Because $\lambda_i\le \lambda _k$ for each $i\in \{1,\cdots, n\}$.
Apr
11
revised A trace inequality with epsilon in Sobolev spaces
edited tags
Apr
10
comment Approximating $u \in H^1$ s.t. $u(T)=0$ with $u_n \in H^1_0$ in the gradient norm?
The space $H_0^1(0,T)$ is complete with the norm $\|u\|=\|\nabla u\|_2$, therefore, if $u\in H_0^1(0,T)$ is such that $\nabla u_n\to \nabla u$ in $L^2$, we must conclude that $u\in H_0^1(0,T)$.
Apr
8
comment Prove that $\dfrac{g(x,u_{n})}{\left\Vert u_{n}\right\Vert ^{p-1}}\rightarrow g_{0}$ weakly in $L^{\overline{p}}$ for some $\overline{p}>p*'$
Where do you got this problem?
Apr
8
comment Complicated convergence of nonlinear term
No @Kamil. I fail to see why does that functions belong to $L^1$. Do you know why?
Apr
7
comment Proof that $C^{\infty}_0$ is dense in $W^{1,p}(\mathbb{R}^n)$
This is the content of Theorem 9.2. in the Brezis book of Functional Analysis,
Apr
7
comment How to prove Poincaré-like inequality for the integral over the boundary?
Why do you think this is true?
Apr
7
comment Complicated convergence of nonlinear term
Why does $|\nabla u_k|^{p-2}\nabla u_k^i u_k^j \cdot \nabla v\in L^1$?
Apr
7
comment How to prove Poincare-like inequality?
Edit it and ask on meta to reopen, or just edit it and I will vote to reopen.
Apr
7
comment How to prove Poincare-like inequality?
There is no need to ask the same question. Just follow the instructions given for the closure of the last one and then hit the button reopen. Take a look in @Pedro's comment.
Apr
6
comment Trace operator on $W^{1,\infty}$
The space $W^{1,\infty}(\Omega)$ is the space of Lipschitz functions defined in $\overline{\Omega}$.
Apr
1
reviewed Leave Open Proving that for when AB = 2BA, then B is not invertible if A is invertible.
Apr
1
reviewed Close Help showing $\sum_{n=2}^{\infty}(\log n)^{-\log n}$ converges.
Apr
1
reviewed Close Does uniform convergence imply $L^1$-convergence?
Apr
1
reviewed Close Find all complex numbers such that $z^4 = 8\bar{z}$
Apr
1
reviewed Close Set of measure $0$ in $[0,1]$ is nowhere dense