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for questions involving inequalities, upper and lower bounds.

1 vote

Sobolev spaces based on $L^p$ with $0<p<1$

The paper (and this comment on it) Peetre, Jaak. A remark on Sobolev spaces. The case $0<p<1$. Collection of articles dedicated to G. G. Lorentz on the occasion of his sixty-fifth birthday, III. J …
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An inequality on concave functions

That $\log \circ f$ is concave follows from concavity of $\log$ and $f$ because $f$ is non-decreasing. I do not see how you could put positivity to use here.
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An inequality on concave functions

We want $$f(x)f(stx)\le f(sx)f(tx)$$ for concave non-decreasing functions with $f(0) = 0$. Since we require this for every $x$ and $f$ we can assume $x = 1$, because our claim is invariant w.r.t scali …
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Numerical analysis of parabolic obstacle problem

In particular, this book references chapter 6 of Roland Glowinski, Jacques-Louis Lions, and Raymond Trémolières, MR 1333916 Numerical analysis of variational inequalities, ISBN: 0-444-86199-8. …
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