Recent content by Tatianaoo

Thanks a lot for clarifying this! Maybe there is some extra condition (except being compactly embedded) that subspace needs to satisfy in order to be dense? Or somebody could suggest nice book about this subject?

True. By compact embedding I mean the following: let (X,||\cdot||),~(Y,||\cdot||) be Banacch spaces and X\subseteq Y. We say that X is compactly embedded in Y if the identity operator i:X\rightarrow Y is compact. Actually by dense embedding I mean usual density of one space in another (a...

Is there any relation between compact embedding and dense embedding? Thanks in advance for your reply.

Thanks!

Hi! Does anybody know if there is something in common between Bernstein functions and Bernstein polynomials except the word 'Bernstein'? I mean from mathematical point of view.

Thanks a lot for help!

Does anybody know if the following is true? Let $p>1$. If $f=f(x,y)$ is such that $f\in L^p([a,b]\times [a,b])$, then $f_y(x)\in L^p([a,b])$ for almost all $y\in[a,b]$ and $f_x(y)\in L^p([a,b])$ for almost all $x\in[a,b]$. Is this a consequence of Fubini's theorem?

Thank you very much for your response. I was thinking about the following problem: we look for the minimizer of the following variational functional \begin{equation*} \mathcal{J}[u]= \int_a^b F(u,\dot{u},t) dt , \end{equation*} subject to the boundary conditions \begin{equation*}...

Does anybody know where can I find theorem ensuring the existence of minimizers for isoperimetric problems? I also need the proof.