All Questions

Does there exist a (onedimensional) integral functional of calculus of variations (with $f$ finite everywhere) $$ F(y)=\int_a^b f(t,y(t),y'(t))\,dt
 $$ such that $$ \inf_{y\in Lip([a,b])}F(y)<\inf_{...

For $f\in C^{1}(\mathbb{R}^{n})$, Gross's logarithmic Sobolev inequality says that $$\int f^{2} \log f^{2}\,d\mu -\int f^{2}\,d\mu \log\left(\int f^{2}\,d\mu\right)\leq \frac{2}{c}\int |\nabla f|^{2}...

The Riesz representation is very useful in study BV space. There is a lot of version of it and one of the good one can be found in this book, page 49. Here I come up with a question which has similar ...